##### Leader of the research group: Michał Horodecki

Post-docs: Paweł Mazurek, John Selby

PhD students: Tanmoy Biswas, Marek Winczewski

The group New Quantum Resources II deals with a broad spectrum of topics, related to such resources as nonlocality/contextuality, entanglement, randomness, athermality, and others.

## Activity

Specific research tasks of the group include:

1) Quantum open systems and quantum thermodynamics

a. Open problems on Thermal Operations

b. Efficiencies of engines based on Thermal Operations

c. The notion of work in micro regime; quantum batteries

d. Dynamical description of thermal quantum machines in various systems, including solar cells, thermoelectric generators, life-harvesting systems

e. Thermodynamics with explicit battery; fluctuation relations

f. Study limitations of Markovian evolution in thermodynamical context

2) Resources for quantum computing:

a. Contextuality/nonlocality, their relation to quantum speedup (in collaboration with NRQ)

b. Quantum gates, t-designs, random circuits.

c. POVMs – their power versus von Neumann measurements and application to quantum algorithms

3) Quantum communication:

a. Port based teleportation – various variants, related group representation problems

b. Quantum error correction

c. Randomness amplification/extraction, secret key extraction (in collaboration with NRQ)

4) Bell inequalities

a. Employing graph theoretic tools

b. Large violation

## Publications

### 2021

- John H. Selby, Carlo Maria Scandolo, and Bob Coecke. Reconstructing quantum theory from diagrammatic postulates.
*Quantum*, 5:445, apr 2021. doi:10.22331/q-2021-04-28-445

[BibTeX] [Abstract] [Download PDF]

A reconstruction of quantum theory refers to both a mathematical and a conceptual paradigm that allows one to derive the usual formulation of quantum theory from a set of primitive assumptions. The motivation for doing so is a discomfort with the usual formulation of quantum theory, a discomfort that started with its originator John von Neumann. We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically appealing. Again equivalently, they are stated in process-theoretic terms, establishing that the conceptual backbone of quantum theory concerns the manner in which systems and processes compose. Aside from the diagrammatic form, the key novel aspect of this reconstruction is the introduction of a new postulate, symmetric purification. Unlike the ordinary purification postulate, symmetric purification applies equally well to classical theory as well as quantum theory. Therefore we first reconstruct the full process theoretic description of quantum theory, consisting of composite classical-quantum systems and their interactions, before restricting ourselves to just the ‘fully quantum’ systems as the final step. We propose two novel alternative manners of doing so, ‘no-leaking’ (roughly that information gain causes disturbance) and ‘purity of cups’ (roughly the existence of entangled states). Interestingly, these turn out to be equivalent in any process theory with cups & caps. Additionally, we show how the standard purification postulate can be seen as an immediate consequence of the symmetric purification postulate and purity of cups. Other tangential results concern the specific frameworks of generalised probabilistic theories (GPTs) and process theories (a.k.a. CQM). Firstly, we provide a diagrammatic presentation of GPTs, which, henceforth, can be subsumed under process theories. Secondly, we argue that the ‘sharp dagger’ is indeed the right choice of a dagger structure as this sharpness is vital to the reconstruction.

`@article{selby_reconstructing_2021, title = {Reconstructing quantum theory from diagrammatic postulates}, volume = {5}, issn = {2521-327X}, url = {https://quantum-journal.org/papers/q-2021-04-28-445/}, doi = {10.22331/q-2021-04-28-445}, abstract = {A reconstruction of quantum theory refers to both a mathematical and a conceptual paradigm that allows one to derive the usual formulation of quantum theory from a set of primitive assumptions. The motivation for doing so is a discomfort with the usual formulation of quantum theory, a discomfort that started with its originator John von Neumann. We present a reconstruction of finite-dimensional quantum theory where all of the postulates are stated in diagrammatic terms, making them intuitive. Equivalently, they are stated in category-theoretic terms, making them mathematically appealing. Again equivalently, they are stated in process-theoretic terms, establishing that the conceptual backbone of quantum theory concerns the manner in which systems and processes compose. Aside from the diagrammatic form, the key novel aspect of this reconstruction is the introduction of a new postulate, symmetric purification. Unlike the ordinary purification postulate, symmetric purification applies equally well to classical theory as well as quantum theory. Therefore we first reconstruct the full process theoretic description of quantum theory, consisting of composite classical-quantum systems and their interactions, before restricting ourselves to just the ‘fully quantum’ systems as the final step. We propose two novel alternative manners of doing so, ‘no-leaking’ (roughly that information gain causes disturbance) and ‘purity of cups’ (roughly the existence of entangled states). Interestingly, these turn out to be equivalent in any process theory with cups \& caps. Additionally, we show how the standard purification postulate can be seen as an immediate consequence of the symmetric purification postulate and purity of cups. Other tangential results concern the specific frameworks of generalised probabilistic theories (GPTs) and process theories (a.k.a. CQM). Firstly, we provide a diagrammatic presentation of GPTs, which, henceforth, can be subsumed under process theories. Secondly, we argue that the ‘sharp dagger’ is indeed the right choice of a dagger structure as this sharpness is vital to the reconstruction.}, language = {en}, urldate = {2021-05-10}, journal = {Quantum}, author = {Selby, John H. and Scandolo, Carlo Maria and Coecke, Bob}, month = apr, year = {2021}, pages = {445}, }`

- David Schmid, John H. Selby, Elie Wolfe, Ravi Kunjwal, and Robert W. Spekkens. Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories.
*PRX Quantum*, 2(1):10331, feb 2021. doi:10.1103/PRXQuantum.2.010331

[BibTeX] [Download PDF]`@Article{schmid_characterization_2021, author = {Schmid, David and Selby, John H. and Wolfe, Elie and Kunjwal, Ravi and Spekkens, Robert W.}, journal = {P{RX} {Q}uantum}, title = {Characterization of {Noncontextuality} in the {Framework} of {Generalized} {Probabilistic} {Theories}}, year = {2021}, issn = {2691-3399}, month = feb, number = {1}, pages = {010331}, volume = {2}, doi = {10.1103/PRXQuantum.2.010331}, language = {en}, url = {https://link.aps.org/doi/10.1103/PRXQuantum.2.010331}, urldate = {2021-05-10}, }`

- Patryk Lipka-Bartosik, Paweł Mazurek, and Michał Horodecki. Second law of thermodynamics for batteries with vacuum state.
*Quantum*, 5:408, mar 2021. doi:10.22331/q-2021-03-10-408

[BibTeX] [Abstract] [Download PDF]

In stochastic thermodynamics work is a random variable whose average is bounded by the change in the free energy of the system. In most treatments, however, the work reservoir that absorbs this change is either tacitly assumed or modelled using unphysical systems with unbounded Hamiltonians (i.e. the ideal weight). In this work we describe the consequences of introducing the ground state of the battery and hence — of breaking its translational symmetry. The most striking consequence of this shift is the fact that the Jarzynski identity is replaced by a family of inequalities. Using these inequalities we obtain corrections to the second law of thermodynamics which vanish exponentially with the distance of the initial state of the battery to the bottom of its spectrum. Finally, we study an exemplary thermal operation which realizes the approximate Landauer erasure and demonstrate the consequences which arise when the ground state of the battery is explicitly introduced. In particular, we show that occupation of the vacuum state of any physical battery sets a lower bound on fluctuations of work, while batteries without vacuum state allow for fluctuation-free erasure.

`@Article{lipka-bartosik_second_2021, author = {Lipka-Bartosik, Patryk and Mazurek, Paweł and Horodecki, Michał}, journal = {Quantum}, title = {Second law of thermodynamics for batteries with vacuum state}, year = {2021}, issn = {2521-327X}, month = mar, pages = {408}, volume = {5}, abstract = {In stochastic thermodynamics work is a random variable whose average is bounded by the change in the free energy of the system. In most treatments, however, the work reservoir that absorbs this change is either tacitly assumed or modelled using unphysical systems with unbounded Hamiltonians (i.e. the ideal weight). In this work we describe the consequences of introducing the ground state of the battery and hence — of breaking its translational symmetry. The most striking consequence of this shift is the fact that the Jarzynski identity is replaced by a family of inequalities. Using these inequalities we obtain corrections to the second law of thermodynamics which vanish exponentially with the distance of the initial state of the battery to the bottom of its spectrum. Finally, we study an exemplary thermal operation which realizes the approximate Landauer erasure and demonstrate the consequences which arise when the ground state of the battery is explicitly introduced. In particular, we show that occupation of the vacuum state of any physical battery sets a lower bound on fluctuations of work, while batteries without vacuum state allow for fluctuation-free erasure.}, doi = {10.22331/q-2021-03-10-408}, groups = {Michal_H}, language = {en}, url = {https://quantum-journal.org/papers/q-2021-03-10-408/}, urldate = {2021-05-10}, }`

- Roberto Salazar, Tanmoy Biswas, Jakub Czartowski, Karol Życzkowski, and Paweł Horodecki. Optimal allocation of quantum resources.
*Quantum*, 5:407, mar 2021. doi:10.22331/q-2021-03-10-407

[BibTeX] [Abstract] [Download PDF]

The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.

`@Article{salazar_optimal_2021, author = {Salazar, Roberto and Biswas, Tanmoy and Czartowski, Jakub and Życzkowski, Karol and Horodecki, Paweł}, journal = {Quantum}, title = {Optimal allocation of quantum resources}, year = {2021}, issn = {2521-327X}, month = mar, pages = {407}, volume = {5}, abstract = {The optimal allocation of resources is a crucial task for their efficient use in a wide range of practical applications in science and engineering. This paper investigates the optimal allocation of resources in multipartite quantum systems. In particular, we show the relevance of proportional fairness and optimal reliability criteria for the application of quantum resources. Moreover, we present optimal allocation solutions for an arbitrary number of qudits using measurement incompatibility as an exemplary resource theory. Besides, we study the criterion of optimal equitability and demonstrate its relevance to scenarios involving several resource theories such as nonlocality vs local contextuality. Finally, we highlight the potential impact of our results for quantum networks and other multi-party quantum information processing, in particular to the future Quantum Internet.}, doi = {10.22331/q-2021-03-10-407}, groups = {Pawel_H}, language = {en}, url = {https://quantum-journal.org/papers/q-2021-03-10-407/}, urldate = {2021-07-28}, }`

- Chandan Datta, Tanmoy Biswas, Debashis Saha, and Remigiusz Augusiak. Perfect discrimination of quantum measurements using entangled systems.
*New Journal of Physics*, 23(4):43021, apr 2021. doi:10.1088/1367-2630/abecaf

[BibTeX] [Download PDF]`@Article{datta_perfect_2021, author = {Datta, Chandan and Biswas, Tanmoy and Saha, Debashis and Augusiak, Remigiusz}, journal = {New {J}ournal of {P}hysics}, title = {Perfect discrimination of quantum measurements using entangled systems}, year = {2021}, issn = {1367-2630}, month = apr, number = {4}, pages = {043021}, volume = {23}, doi = {10.1088/1367-2630/abecaf}, url = {https://iopscience.iop.org/article/10.1088/1367-2630/abecaf}, urldate = {2021-07-28}, }`

### 2020

- Paweł Mazurek, Máté. Farkas, Andrzej Grudka, Michał Horodecki, and Michał Studziński. Quantum error-correction codes and absolutely maximally entangled states.
*Physical Review A*, 101(4):42305, 2020. doi:10.1103/PhysRevA.101.042305

[BibTeX] [Download PDF]`@Article{mazurek_quantum_2020, author = {Mazurek, Paweł and Farkas, Máté and Grudka, Andrzej and Horodecki, Michał and Studziński, Michał}, journal = {Physical {R}eview {A}}, title = {Quantum error-correction codes and absolutely maximally entangled states}, year = {2020}, issn = {2469-9926, 2469-9934}, month = apr, number = {4}, pages = {042305}, volume = {101}, doi = {10.1103/PhysRevA.101.042305}, groups = {Michal_H}, language = {en}, url = {https://link.aps.org/doi/10.1103/PhysRevA.101.042305}, urldate = {2020-04-22}, }`

- Monika Rosicka, Paweł Mazurek, Andrzej Grudka, and Michał Horodecki. Generalized XOR non-locality games with graph description on a square lattice.
*Journal of Physics A: Mathematical and Theoretical*, 53(26):265302, jul 2020. doi:10.1088/1751-8121/ab8f3e

[BibTeX] [Download PDF]`@Article{rosicka_generalized_2020, author = {Rosicka, Monika and Mazurek, Paweł and Grudka, Andrzej and Horodecki, Michał}, journal = {Journal of {P}hysics {A}: {M}athematical and {T}heoretical}, title = {Generalized {XOR} non-locality games with graph description on a square lattice}, year = {2020}, issn = {1751-8113, 1751-8121}, month = jul, number = {26}, pages = {265302}, volume = {53}, doi = {10.1088/1751-8121/ab8f3e}, groups = {Michal_H}, url = {https://iopscience.iop.org/article/10.1088/1751-8121/ab8f3e}, urldate = {2020-06-24}, }`

- Debashis Saha, Michał Oszmaniec, Łukasz Czekaj, Michał Horodecki, and Ryszard Horodecki. Operational foundations for complementarity and uncertainty relations.
*Physical Review A*, 101(5):52104, 2020. doi:10.1103/PhysRevA.101.052104

[BibTeX] [Download PDF]`@Article{saha_operational_2020, author = {Saha, Debashis and Oszmaniec, Michał and Czekaj, Łukasz and Horodecki, Michał and Horodecki, Ryszard}, journal = {Physical {R}eview {A}}, title = {Operational foundations for complementarity and uncertainty relations}, year = {2020}, issn = {2469-9926, 2469-9934}, month = may, number = {5}, pages = {052104}, volume = {101}, doi = {10.1103/PhysRevA.101.052104}, groups = {Michal_H}, language = {en}, url = {https://link.aps.org/doi/10.1103/PhysRevA.101.052104}, urldate = {2021-05-10}, }`

- Ravishankar Ramanathan, Monika Rosicka, Karol Horodecki, Stefano Pironio, Michał Horodecki, and Paweł Horodecki. Gadget structures in proofs of the Kochen-Specker theorem.
*Quantum*, 4:308, aug 2020. doi:10.22331/q-2020-08-14-308

[BibTeX] [Abstract] [Download PDF]

The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term 01 -gadgets, that capture the essential contradiction necessary to prove the Kochen-Specker theorem, i.e,. every Kochen-Specker graph contains a 01 -gadget and from every 01 -gadget one can construct a proof of the Kochen-Specker theorem. Moreover, we show that the 01 -gadgets form a fundamental primitive that can be used to formulate state-independent and state-dependent statistical Kochen-Specker arguments as well as to give simple constructive proofs of an “extended” Kochen-Specker theorem first considered by Pitowsky in {\textbackslash}cite\{Pitowsky\}.

`@Article{ramanathan_gadget_2020, author = {Ramanathan, Ravishankar and Rosicka, Monika and Horodecki, Karol and Pironio, Stefano and Horodecki, Michał and Horodecki, Paweł}, journal = {Quantum}, title = {Gadget structures in proofs of the {Kochen}-{Specker} theorem}, year = {2020}, issn = {2521-327X}, month = aug, pages = {308}, volume = {4}, abstract = {The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term 01 -gadgets, that capture the essential contradiction necessary to prove the Kochen-Specker theorem, i.e,. every Kochen-Specker graph contains a 01 -gadget and from every 01 -gadget one can construct a proof of the Kochen-Specker theorem. Moreover, we show that the 01 -gadgets form a fundamental primitive that can be used to formulate state-independent and state-dependent statistical Kochen-Specker arguments as well as to give simple constructive proofs of an ``extended'' Kochen-Specker theorem first considered by Pitowsky in {\textbackslash}cite\{Pitowsky\}.}, doi = {10.22331/q-2020-08-14-308}, groups = {Pawel_H, Michal_H}, language = {en}, url = {https://quantum-journal.org/papers/q-2020-08-14-308/}, urldate = {2021-05-10}, }`

- Omer Sakarya, Marek Winczewski, Adam Rutkowski, and Karol Horodecki. Hybrid quantum network design against unauthorized secret-key generation, and its memory cost.
*Physical Review Research*, 2(4):43022, oct 2020. doi:10.1103/PhysRevResearch.2.043022

[BibTeX] [Download PDF]`@Article{sakarya_hybrid_2020, author = {Sakarya, Omer and Winczewski, Marek and Rutkowski, Adam and Horodecki, Karol}, journal = {Physical {R}eview {R}esearch}, title = {Hybrid quantum network design against unauthorized secret-key generation, and its memory cost}, year = {2020}, issn = {2643-1564}, month = oct, number = {4}, pages = {043022}, volume = {2}, doi = {10.1103/PhysRevResearch.2.043022}, language = {en}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.043022}, urldate = {2021-05-10}, }`

- John H. Selby and Ciarán M. Lee. Compositional resource theories of coherence.
*Quantum*, 4:319, sep 2020. doi:10.22331/q-2020-09-11-319

[BibTeX] [Abstract] [Download PDF]

Quantum coherence is one of the most important resources in quantum information theory. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers. Recently, there has been substantial progress in developing mathematical resource theories of coherence, paving the way towards its quantification and control. To date however, these resource theories have only been mathematically formalised within the realms of convex-geometry, information theory, and linear algebra. This approach is limited in scope, and makes it difficult to generalise beyond resource theories of coherence for single system quantum states. In this paper we take a complementary perspective, showing that resource theories of coherence can instead be defined purely compositionally, that is, working with the mathematics of process theories, string diagrams and category theory. This new perspective offers several advantages: i) it unifies various existing approaches to the study of coherence, for example, subsuming both speakable and unspeakable coherence; ii) it provides a general treatment of the compositional multi-system setting; iii) it generalises immediately to the case of quantum channels, measurements, instruments, and beyond rather than just states; iv) it can easily be generalised to the setting where there are multiple distinct sources of decoherence; and, iv) it directly extends to arbitrary process theories, for example, generalised probabilistic theories and Spekkens toy model–-providing the ability to operationally characterise coherence rather than relying on specific mathematical features of quantum theory for its description. More importantly, by providing a new, complementary, perspective on the resource of coherence, this work opens the door to the development of novel tools which would not be accessible from the linear algebraic mind set.

`@article{selby_compositional_2020, title = {Compositional resource theories of coherence}, volume = {4}, issn = {2521-327X}, url = {https://quantum-journal.org/papers/q-2020-09-11-319/}, doi = {10.22331/q-2020-09-11-319}, abstract = {Quantum coherence is one of the most important resources in quantum information theory. Indeed, preventing the loss of coherence is one of the most important technical challenges obstructing the development of large-scale quantum computers. Recently, there has been substantial progress in developing mathematical resource theories of coherence, paving the way towards its quantification and control. To date however, these resource theories have only been mathematically formalised within the realms of convex-geometry, information theory, and linear algebra. This approach is limited in scope, and makes it difficult to generalise beyond resource theories of coherence for single system quantum states. In this paper we take a complementary perspective, showing that resource theories of coherence can instead be defined purely compositionally, that is, working with the mathematics of process theories, string diagrams and category theory. This new perspective offers several advantages: i) it unifies various existing approaches to the study of coherence, for example, subsuming both speakable and unspeakable coherence; ii) it provides a general treatment of the compositional multi-system setting; iii) it generalises immediately to the case of quantum channels, measurements, instruments, and beyond rather than just states; iv) it can easily be generalised to the setting where there are multiple distinct sources of decoherence; and, iv) it directly extends to arbitrary process theories, for example, generalised probabilistic theories and Spekkens toy model---providing the ability to operationally characterise coherence rather than relying on specific mathematical features of quantum theory for its description. More importantly, by providing a new, complementary, perspective on the resource of coherence, this work opens the door to the development of novel tools which would not be accessible from the linear algebraic mind set.}, language = {en}, urldate = {2021-05-10}, journal = {Quantum}, author = {Selby, John H. and Lee, Ciarán M.}, month = sep, year = {2020}, pages = {319}, }`

- Jamie Sikora and John H. Selby. Impossibility of coin flipping in generalized probabilistic theories via discretizations of semi-infinite programs.
*Physical Review Research*, 2(4):43128, oct 2020. doi:10.1103/PhysRevResearch.2.043128

[BibTeX] [Download PDF]`@Article{sikora_impossibility_2020, author = {Sikora, Jamie and Selby, John H.}, journal = {Physical {R}eview {R}esearch}, title = {Impossibility of coin flipping in generalized probabilistic theories via discretizations of semi-infinite programs}, year = {2020}, issn = {2643-1564}, month = oct, number = {4}, pages = {043128}, volume = {2}, doi = {10.1103/PhysRevResearch.2.043128}, language = {en}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.043128}, urldate = {2021-05-10}, }`

- Marcin Łobejko, Paweł Mazurek, and Michał Horodecki. Thermodynamics of Minimal Coupling Quantum Heat Engines.
*Quantum*, 4:375, dec 2020. arXiv: 2003.05788 doi:10.22331/q-2020-12-23-375

[BibTeX] [Abstract] [Download PDF]

The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes – energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced “control-marginal state” – one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.

`@Article{lobejko_thermodynamics_2020, author = {Łobejko, Marcin and Mazurek, Paweł and Horodecki, Michał}, journal = {Quantum}, title = {Thermodynamics of {Minimal} {Coupling} {Quantum} {Heat} {Engines}}, year = {2020}, issn = {2521-327X}, month = dec, note = {arXiv: 2003.05788}, pages = {375}, volume = {4}, abstract = {The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes -- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to two-body operations make the engine fundamentally irreversible. Our main result is finding the optimal efficiency and work production per cycle within the whole class of irreversible minimal-coupling engines composed of three strokes and with the two-level working body, where we take into account all possible quantum correlations between the working body and the battery. One of the key new tools is the introduced "control-marginal state" -- one which acts only on a working body Hilbert space, but encapsulates all features regarding work extraction of the total working body-battery system. In addition, we propose a generalization of the many-stroke engine, and we analyze efficiency vs extracted work trade-offs, as well as work fluctuations after many cycles of the running of the engine.}, doi = {10.22331/q-2020-12-23-375}, groups = {Michal_H}, keywords = {Quantum Physics}, url = {http://arxiv.org/abs/2003.05788}, urldate = {2021-07-28}, }`

- Piotr Kopszak, Marek Mozrzymas, Michał Studziński, and Michał Horodecki. Multiport based teleportation – transmission of a large amount of quantum information.
*Quantum 5, 576 (2021)*, aug 2020. doi:10.22331/q-2021-11-11-576

[BibTeX] [Abstract] [Download PDF]

We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is effectively computable and outperforms the explicit values of the entanglement fidelity calculated for the pre-existing variants of the port-based protocols, allowing for teleportation of a much larger amount of quantum information. The comparison with the exact formulas and similar analysis for the probabilistic scheme is also discussed. In particular, we present the closed-form expressions for the entanglement fidelity and for the probability of success in the probabilistic scheme in the qubit case in the picture of the spin angular momentum.

`@Article{Kopszak2020, author = {Piotr Kopszak and Marek Mozrzymas and Michał Studziński and Michał Horodecki}, journal = {Quantum 5, 576 (2021)}, title = {Multiport based teleportation -- transmission of a large amount of quantum information}, year = {2020}, month = aug, abstract = {We analyse the problem of transmitting a number of unknown quantum states or one composite system in one go. We derive a lower bound on the performance of such process, measured in the entanglement fidelity. The obtained bound is effectively computable and outperforms the explicit values of the entanglement fidelity calculated for the pre-existing variants of the port-based protocols, allowing for teleportation of a much larger amount of quantum information. The comparison with the exact formulas and similar analysis for the probabilistic scheme is also discussed. In particular, we present the closed-form expressions for the entanglement fidelity and for the probability of success in the probabilistic scheme in the qubit case in the picture of the spin angular momentum.}, archiveprefix = {arXiv}, doi = {10.22331/q-2021-11-11-576}, eprint = {2008.00856}, groups = {Michal_H}, keywords = {quant-ph}, primaryclass = {quant-ph}, url = {http://arxiv.org/pdf/2008.00856v3}, }`

## arXiv preprints

### 2021

- John H. Selby, David Schmid, Elie Wolfe, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens. Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality.
*Arxiv:2112.04521 [quant-ph]*, dec 2021. arXiv: 2112.04521

[BibTeX] [Abstract] [Download PDF]

The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particular experimental setup within a given physical theory. We show that the resulting characterization is not generally a GPT in and of itself-rather, it is described by a more general mathematical object that we introduce and term an accessible GPT fragment. We then introduce an equivalence relation, termed cone equivalence, between accessible GPT fragments (and, as a special case, between standard GPTs). We give a number of examples of experimental scenarios that are best described using accessible GPT fragments, and where moreover cone-equivalence arises naturally. We then prove that an accessible GPT fragment admits of a classical explanation if and only if every other fragment that is cone-equivalent to it also admits of a classical explanation. Finally, we leverage this result to prove several fundamental results regarding the experimental requirements for witnessing the failure of generalized noncontextuality. In particular, we prove that neither incompatibility among measurements nor the assumption of freedom of choice is necessary for witnessing failures of generalized noncontextuality, and, moreover, that such failures can be witnessed even using arbitrarily inefficient detectors.

`@article{selby_accessible_2021, title = {Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality}, url = {https://arxiv.org/abs/2112.04521}, abstract = {The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particular experimental setup within a given physical theory. We show that the resulting characterization is not generally a GPT in and of itself-rather, it is described by a more general mathematical object that we introduce and term an accessible GPT fragment. We then introduce an equivalence relation, termed cone equivalence, between accessible GPT fragments (and, as a special case, between standard GPTs). We give a number of examples of experimental scenarios that are best described using accessible GPT fragments, and where moreover cone-equivalence arises naturally. We then prove that an accessible GPT fragment admits of a classical explanation if and only if every other fragment that is cone-equivalent to it also admits of a classical explanation. Finally, we leverage this result to prove several fundamental results regarding the experimental requirements for witnessing the failure of generalized noncontextuality. In particular, we prove that neither incompatibility among measurements nor the assumption of freedom of choice is necessary for witnessing failures of generalized noncontextuality, and, moreover, that such failures can be witnessed even using arbitrarily inefficient detectors.}, urldate = {2021-12-10}, journal = {arXiv:2112.04521 [quant-ph]}, author = {Selby, John H. and Schmid, David and Wolfe, Elie and Sainz, Ana Belén and Kunjwal, Ravi and Spekkens, Robert W.}, month = dec, year = {2021}, note = {arXiv: 2112.04521}, keywords = {Quantum Physics}, }`

- David Schmid, Haoxing Du, John H. Selby, and Matthew F. Pusey. The only noncontextual model of the stabilizer subtheory is Gross’s.
*Arxiv:2101.06263 [quant-ph]*, feb 2021. arXiv: 2101.06263

[BibTeX] [Abstract] [Download PDF]

We prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross’s discrete Wigner function. This representation is equivalent to Spekkens’ epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model for the stabilizer subtheory. Strikingly, the principle of noncontextuality is powerful enough (at least in this setting) to single out one particular classical realist interpretation. Our result explains the practical utility of Gross’s representation, e.g. why (in the setting of the stabilizer subtheory) negativity in this particular representation implies generalized contextuality, and hence sheds light on why negativity of this particular representation is a resource for quantum computational speedup. It also allows us to prove that generalized contextuality is a necessary resource for universal quantum computation in the state injection model. In all even dimensions, we prove that there does not exist any nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory, and, hence, that the stabilizer subtheory is contextual in all even dimensions. Together, these results constitute a complete characterization of the (non)classicality of all stabilizer subtheories.

`@article{schmid_only_2021, title = {The only noncontextual model of the stabilizer subtheory is {Gross}'s}, url = {http://arxiv.org/abs/2101.06263}, abstract = {We prove that there is a unique nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory in all odd dimensions, namely Gross's discrete Wigner function. This representation is equivalent to Spekkens' epistemically restricted toy theory, which is consequently singled out as the unique noncontextual ontological model for the stabilizer subtheory. Strikingly, the principle of noncontextuality is powerful enough (at least in this setting) to single out one particular classical realist interpretation. Our result explains the practical utility of Gross's representation, e.g. why (in the setting of the stabilizer subtheory) negativity in this particular representation implies generalized contextuality, and hence sheds light on why negativity of this particular representation is a resource for quantum computational speedup. It also allows us to prove that generalized contextuality is a necessary resource for universal quantum computation in the state injection model. In all even dimensions, we prove that there does not exist any nonnegative and diagram-preserving quasiprobability representation of the stabilizer subtheory, and, hence, that the stabilizer subtheory is contextual in all even dimensions. Together, these results constitute a complete characterization of the (non)classicality of all stabilizer subtheories.}, urldate = {2021-07-28}, journal = {arXiv:2101.06263 [quant-ph]}, author = {Schmid, David and Du, Haoxing and Selby, John H. and Pusey, Matthew F.}, month = feb, year = {2021}, note = {arXiv: 2101.06263}, keywords = {Quantum Physics}, }`

- Thomas D. Galley, Flaminia Giacomini, and John H. Selby. A no-go theorem on the nature of the gravitational field beyond quantum theory.
*Arxiv:2012.01441 [gr-qc, physics:quant-ph]*, 2021. arXiv: 2012.01441

[BibTeX] [Abstract] [Download PDF]

Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled due to solely the gravitational interaction. Typically, this question has been addressed by assuming an underlying physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we introduce the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework has the advantage that it only relies on the set of operationally accessible states, transformations, and measurements, without presupposing an underlying theory. Hence, it provides a framework to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two non-classical systems. Assuming that such entanglement is observed we prove a no-go theorem stating that the following statements are incompatible: i) the two non-classical systems are independent subsystems, ii) the gravitational field is a physical degree of freedom which mediates the interaction and iii) the gravitational field is classical. Moreover we argue that conditions i) and ii) should be met, and hence that the gravitational field is non-classical. Non-classicality does not imply that the gravitational field is quantum, and to illustrate this we provide examples of non-classical and non-quantum theories which are logically consistent with the other conditions.

`@article{galley_no-go_2021, title = {A no-go theorem on the nature of the gravitational field beyond quantum theory}, url = {http://arxiv.org/abs/2012.01441}, abstract = {Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled due to solely the gravitational interaction. Typically, this question has been addressed by assuming an underlying physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we introduce the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework has the advantage that it only relies on the set of operationally accessible states, transformations, and measurements, without presupposing an underlying theory. Hence, it provides a framework to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two non-classical systems. Assuming that such entanglement is observed we prove a no-go theorem stating that the following statements are incompatible: i) the two non-classical systems are independent subsystems, ii) the gravitational field is a physical degree of freedom which mediates the interaction and iii) the gravitational field is classical. Moreover we argue that conditions i) and ii) should be met, and hence that the gravitational field is non-classical. Non-classicality does not imply that the gravitational field is quantum, and to illustrate this we provide examples of non-classical and non-quantum theories which are logically consistent with the other conditions.}, urldate = {2021-07-28}, journal = {arXiv:2012.01441 [gr-qc, physics:quant-ph]}, author = {Galley, Thomas D. and Giacomini, Flaminia and Selby, John H.}, month = jun, year = {2021}, note = {arXiv: 2012.01441}, keywords = {Quantum Physics, General Relativity and Quantum Cosmology}, }`

- David Schmid, John H. Selby, and Robert W. Spekkens. Unscrambling the omelette of causation and inference: The framework of causal-inferential theories.
*Arxiv:2009.03297 [quant-ph]*, may 2021. arXiv: 2009.03297

[BibTeX] [Abstract] [Download PDF]

Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a realist account of an experiment offers beyond an operational account. It also yields a novel characterization of the assumptions and implications of standard no-go theorems for realist representations of operational quantum theory, namely, those based on Bell’s notion of locality and those based on generalized noncontextuality. Moreover, our process-theoretic characterization of generalised noncontextuality is shown to be implied by an even more natural principle which we term Leibnizianity. Most strikingly, our framework offers a way forward in a research program that seeks to circumvent these no-go results. Specifically, we argue that if one can identify axioms for a realist causal-inferential theory such that the notions of causation and inference can differ from their conventional (classical) interpretations, then one has the means of defining an intrinsically quantum notion of realism, and thereby a realist representation of operational quantum theory that salvages the spirit of locality and of noncontextuality.

`@article{schmid_unscrambling_2021, title = {Unscrambling the omelette of causation and inference: {The} framework of causal-inferential theories}, shorttitle = {Unscrambling the omelette of causation and inference}, url = {http://arxiv.org/abs/2009.03297}, abstract = {Using a process-theoretic formalism, we introduce the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. Recasting the notions of operational and realist theories in this mold clarifies what a realist account of an experiment offers beyond an operational account. It also yields a novel characterization of the assumptions and implications of standard no-go theorems for realist representations of operational quantum theory, namely, those based on Bell's notion of locality and those based on generalized noncontextuality. Moreover, our process-theoretic characterization of generalised noncontextuality is shown to be implied by an even more natural principle which we term Leibnizianity. Most strikingly, our framework offers a way forward in a research program that seeks to circumvent these no-go results. Specifically, we argue that if one can identify axioms for a realist causal-inferential theory such that the notions of causation and inference can differ from their conventional (classical) interpretations, then one has the means of defining an intrinsically quantum notion of realism, and thereby a realist representation of operational quantum theory that salvages the spirit of locality and of noncontextuality.}, urldate = {2021-07-28}, journal = {arXiv:2009.03297 [quant-ph]}, author = {Schmid, David and Selby, John H. and Spekkens, Robert W.}, month = may, year = {2021}, note = {arXiv: 2009.03297}, keywords = {Quantum Physics}, }`

- John H. Selby, Ana Belén Sainz, and Paweł Horodecki. Revisiting dynamics of quantum causal structures – when can causal order evolve?.
*Arxiv:2008.12757 [quant-ph]*, mar 2021. arXiv: 2008.12757

[BibTeX] [Abstract] [Download PDF]

Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)] pursues this using the process matrix formalism, together with a definition of the possible dynamics of such process matrices, and focusing especially on the question of evolution of causal structures. One of its major conclusions is a strong theorem saying that, within the formalism, under continuous and reversible transformations, the causal order between operations must be preserved. Here we find a surprising result: if one is to take into account a full picture of the physical evolution of operations within the standard quantum-mechanical formalism, then one can actually draw the opposite conclusion. That is, we show that under certain continuous and reversible dynamics the causal order between operations is not necessarily preserved. We moreover identify and analyse the root of this apparent contradiction, specifically, that the commonly accepted and widely applied framework of higher-order processes, whilst mathematically sound, is not always appropriate for drawing conclusions on the fundamentals of physical dynamics. Finally we show how to reconcile the elements of the whole picture following the intuition based on entanglement processing by local operations and classical communication.

`@Article{selby_revisiting_2021, author = {Selby, John H. and Sainz, Ana Belén and Horodecki, Paweł}, journal = {arXiv:2008.12757 [quant-ph]}, title = {Revisiting dynamics of quantum causal structures -- when can causal order evolve?}, year = {2021}, month = mar, note = {arXiv: 2008.12757}, abstract = {Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)] pursues this using the process matrix formalism, together with a definition of the possible dynamics of such process matrices, and focusing especially on the question of evolution of causal structures. One of its major conclusions is a strong theorem saying that, within the formalism, under continuous and reversible transformations, the causal order between operations must be preserved. Here we find a surprising result: if one is to take into account a full picture of the physical evolution of operations within the standard quantum-mechanical formalism, then one can actually draw the opposite conclusion. That is, we show that under certain continuous and reversible dynamics the causal order between operations is not necessarily preserved. We moreover identify and analyse the root of this apparent contradiction, specifically, that the commonly accepted and widely applied framework of higher-order processes, whilst mathematically sound, is not always appropriate for drawing conclusions on the fundamentals of physical dynamics. Finally we show how to reconcile the elements of the whole picture following the intuition based on entanglement processing by local operations and classical communication.}, groups = {Pawel_H}, keywords = {Quantum Physics}, url = {http://arxiv.org/abs/2008.12757}, urldate = {2021-07-28}, }`

- Paulo J. Cavalcanti, John H. Selby, Jamie Sikora, Thomas D. Galley, and Ana Belén Sainz. Witworld: A generalised probabilistic theory featuring post-quantum steering.
*Arxiv:2102.06581 [quant-ph]*, feb 2021. arXiv: 2102.06581

[BibTeX] [Abstract] [Download PDF]

We introduce Witworld: a generalised probabilistic theory with strong post-quantum features, which subsumes Boxworld. Witworld is the first theory that features post-quantum steering, and also the first that outperforms quantum theory at the task of remote state preparation. We further show post-quantum steering to be the source of this advantage, and hence present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing.

`@article{cavalcanti_witworld:_2021, title = {Witworld: {A} generalised probabilistic theory featuring post-quantum steering}, shorttitle = {Witworld}, url = {http://arxiv.org/abs/2102.06581}, abstract = {We introduce Witworld: a generalised probabilistic theory with strong post-quantum features, which subsumes Boxworld. Witworld is the first theory that features post-quantum steering, and also the first that outperforms quantum theory at the task of remote state preparation. We further show post-quantum steering to be the source of this advantage, and hence present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing.}, urldate = {2021-07-28}, journal = {arXiv:2102.06581 [quant-ph]}, author = {Cavalcanti, Paulo J. and Selby, John H. and Sikora, Jamie and Galley, Thomas D. and Sainz, Ana Belén}, month = feb, year = {2021}, note = {arXiv: 2102.06581}, keywords = {Quantum Physics}, }`

- Tanmoy Biswas, Oliveira A. de Junior, Michał Horodecki, and Kamil Korzekwa. Fluctuation-dissipation relations for thermodynamic distillation processes.
*Arxiv:2105.11759 [quant-ph]*, 5 2021.

[BibTeX] [Abstract] [Download PDF]

The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterise optimal thermodynamic distillation processes, and then prove a relation between the amount of free energy dissipated in such processes and the free energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or arbitrary number of independent energy-incoherent systems, and allow not only for a state transformation, but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure and thermodynamically-free communication, up to second-order asymptotics in the number $N$ of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite $N$.

`@Article{Biswas2021a, author = {Biswas, Tanmoy and Junior, A. de Oliveira and Horodecki, Michał and Korzekwa, Kamil}, journal = {arXiv:2105.11759 [quant-ph]}, title = {Fluctuation-dissipation relations for thermodynamic distillation processes}, year = {2021}, month = {5}, abstract = {The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterise optimal thermodynamic distillation processes, and then prove a relation between the amount of free energy dissipated in such processes and the free energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or arbitrary number of independent energy-incoherent systems, and allow not only for a state transformation, but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure and thermodynamically-free communication, up to second-order asymptotics in the number $N$ of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite $N$.}, archiveprefix = {arXiv}, eprint = {2105.11759}, groups = {Michal_H}, keywords = {Quantum Physics, Condensed Matter - Statistical Mechanics}, primaryclass = {quant-ph}, url = {https://arxiv.org/pdf/2105.11759}, }`

- Karol Horodecki, Marek Winczewski, and Siddhartha Das. Fundamental limitations on device-independent quantum conference key agreement.
*Arxiv e-prints*, pages arXiv:2111.02467, nov 2021.

[BibTeX] [Abstract] [Download PDF]

We provide several general upper bounds on device-independent conference key agreement (DI-CKA) against the quantum adversary. They include bounds by reduced entanglement measures and those based on multipartite secrecy monotones such as reduced cc-squashed entanglement. We compare the latter bound with the known lower bound for the protocol of conference key distillation based on the parity-CHSH game. We also show that the gap between DI-CKA rate and the rate of device-dependent is inherited from the bipartite gap between device-independent and device-dependent key rates, giving examples that exhibit the strict gap.

`@Article{Horodecki2021, author = {Horodecki, Karol and Winczewski, Marek and Das, Siddhartha}, journal = {arXiv e-prints}, title = {Fundamental limitations on device-independent quantum conference key agreement}, year = {2021}, month = nov, pages = {arXiv:2111.02467}, abstract = {We provide several general upper bounds on device-independent conference key agreement (DI-CKA) against the quantum adversary. They include bounds by reduced entanglement measures and those based on multipartite secrecy monotones such as reduced cc-squashed entanglement. We compare the latter bound with the known lower bound for the protocol of conference key distillation based on the parity-CHSH game. We also show that the gap between DI-CKA rate and the rate of device-dependent is inherited from the bipartite gap between device-independent and device-dependent key rates, giving examples that exhibit the strict gap.}, archiveprefix = {arXiv}, eid = {arXiv:2111.02467}, eprint = {2111.02467}, keywords = {Quantum Physics, Computer Science - Information Theory, Mathematical Physics}, primaryclass = {quant-ph}, url = {https://arxiv.org/pdf/2111.02467}, }`

### 2020

- David Schmid, John H. Selby, Matthew F. Pusey, and Robert W. Spekkens. A structure theorem for generalized-noncontextual ontological models.
*Arxiv:2005.07161 [quant-ph]*, 2020. arXiv: 2005.07161

[BibTeX] [Abstract] [Download PDF]

It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model. Existing works on generalized noncontextuality have focused on experimental scenarios having a simple structure, typically, prepare-measure scenarios. Here, we formally extend the framework of ontological models as well as the principle of generalized noncontextuality to arbitrary compositional scenarios. We leverage this process-theoretic framework to prove that, under some reasonable assumptions, every generalized-noncontextual ontological model of a tomographically local operational theory has a surprisingly rigid and simple mathematical structure; in short, it corresponds to a frame representation which is not overcomplete. One consequence of this theorem is that the largest number of ontic states possible in any such model is given by the dimension of the associated generalized probabilistic theory. This constraint is useful for generating noncontextuality no-go theorems as well as techniques for experimentally certifying contextuality. Along the way, we extend known results concerning the equivalence of different notions of classicality from prepare-measure scenarios to arbitrary compositional scenarios. Specifically, we prove a correspondence between the following three notions of classical explainability of an operational theory: (i) admitting a noncontextual ontological model, (ii) admitting of a positive quasiprobability representation, and (iii) being simplex-embeddable.

`@article{schmid_structure_2020, title = {A structure theorem for generalized-noncontextual ontological models}, url = {http://arxiv.org/abs/2005.07161}, abstract = {It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model. Existing works on generalized noncontextuality have focused on experimental scenarios having a simple structure, typically, prepare-measure scenarios. Here, we formally extend the framework of ontological models as well as the principle of generalized noncontextuality to arbitrary compositional scenarios. We leverage this process-theoretic framework to prove that, under some reasonable assumptions, every generalized-noncontextual ontological model of a tomographically local operational theory has a surprisingly rigid and simple mathematical structure; in short, it corresponds to a frame representation which is not overcomplete. One consequence of this theorem is that the largest number of ontic states possible in any such model is given by the dimension of the associated generalized probabilistic theory. This constraint is useful for generating noncontextuality no-go theorems as well as techniques for experimentally certifying contextuality. Along the way, we extend known results concerning the equivalence of different notions of classicality from prepare-measure scenarios to arbitrary compositional scenarios. Specifically, we prove a correspondence between the following three notions of classical explainability of an operational theory: (i) admitting a noncontextual ontological model, (ii) admitting of a positive quasiprobability representation, and (iii) being simplex-embeddable.}, urldate = {2020-09-04}, journal = {arXiv:2005.07161 [quant-ph]}, author = {Schmid, David and Selby, John H. and Pusey, Matthew F. and Spekkens, Robert W.}, month = may, year = {2020}, note = {arXiv: 2005.07161}, keywords = {Quantum Physics}, }`

- Ravishankar Ramanathan, Michał Horodecki, Hammad Anwer, Stefano Pironio, Karol Horodecki, Marcus Grünfeld, Sadiq Muhammad, Mohamed Bourennane, and Paweł Horodecki. Practical No-Signalling proof Randomness Amplification using Hardy paradoxes and its experimental implementation.
*Arxiv:1810.11648 [quant-ph]*, 2020. arXiv: 1810.11648

[BibTeX] [Abstract] [Download PDF]

Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-signalling proof protocols for this fundamental task have thus far relied on esoteric proofs of non-locality termed pseudo-telepathy games, complicated multi-party setups or high-dimensional quantum systems, and have remained out of reach of experimental implementation. In this paper, we construct the first practically relevant no-signalling proof DI protocols for randomness amplification based on the simplest proofs of Bell non-locality and illustrate them with an experimental implementation in a quantum optical setup using polarised photons. Technically, we relate the problem to the vast field of Hardy paradoxes, without which it would be impossible to achieve amplification of arbitrarily weak sources in the simplest Bell non-locality scenario consisting of two parties choosing between two binary inputs. Furthermore, we identify a deep connection between proofs of the celebrated Kochen-Specker theorem and Hardy paradoxes that enables us to construct Hardy paradoxes with the non-zero probability taking any value in \$(0,1]\$. Our methods enable us, under the fair-sampling assumption of the experiment, to realize up to \$25\$ bits of randomness in \$20\$ hours of experimental data collection from an initial private source of randomness \$0.1\$ away from uniform.

`@Article{ramanathan_practical_2020, author = {Ramanathan, Ravishankar and Horodecki, Michał and Anwer, Hammad and Pironio, Stefano and Horodecki, Karol and Grünfeld, Marcus and Muhammad, Sadiq and Bourennane, Mohamed and Horodecki, Paweł}, journal = {arXiv:1810.11648 [quant-ph]}, title = {Practical {No}-{Signalling} proof {Randomness} {Amplification} using {Hardy} paradoxes and its experimental implementation}, year = {2020}, month = sep, note = {arXiv: 1810.11648}, abstract = {Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-signalling proof protocols for this fundamental task have thus far relied on esoteric proofs of non-locality termed pseudo-telepathy games, complicated multi-party setups or high-dimensional quantum systems, and have remained out of reach of experimental implementation. In this paper, we construct the first practically relevant no-signalling proof DI protocols for randomness amplification based on the simplest proofs of Bell non-locality and illustrate them with an experimental implementation in a quantum optical setup using polarised photons. Technically, we relate the problem to the vast field of Hardy paradoxes, without which it would be impossible to achieve amplification of arbitrarily weak sources in the simplest Bell non-locality scenario consisting of two parties choosing between two binary inputs. Furthermore, we identify a deep connection between proofs of the celebrated Kochen-Specker theorem and Hardy paradoxes that enables us to construct Hardy paradoxes with the non-zero probability taking any value in \$(0,1]\$. Our methods enable us, under the fair-sampling assumption of the experiment, to realize up to \$25\$ bits of randomness in \$20\$ hours of experimental data collection from an initial private source of randomness \$0.1\$ away from uniform.}, groups = {Michal_H, Pawel_H}, keywords = {Quantum Physics}, url = {http://arxiv.org/abs/1810.11648}, urldate = {2021-05-11}, }`

- Łukasz Czekaj, Ana Belén Sainz, John Selby, and Michał Horodecki. Correlations constrained by composite measurements.
*Arxiv:2009.04994 [quant-ph]*, sep 2020. arXiv: 2009.04994

[BibTeX] [Abstract] [Download PDF]

How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations that physical theories may feature when restricted by some particular constraints on their measurements. We show that demanding that a theory exhibits a composite measurement imposes a hierarchy of constraints on the structure of its sets of states and effects, which translate to a hierarchy of constraints on the allowed correlations themselves. We moreover focus on the particular case where one demands the existence of an entangled measurement that reads out the parity of local fiducial measurements. By formulating a non-linear Optimisation Problem, and semidefinite relaxations of it, we explore the consequences of the existence of such a parity reading measurement for violations of Bell inequalities. In particular, we show that in certain situations this assumption has surprisingly strong consequences, namely, that Tsirelson’s bound can be recovered.

`@Article{czekaj_correlations_2020, author = {Czekaj, Łukasz and Sainz, Ana Belén and Selby, John and Horodecki, Michał}, journal = {arXiv:2009.04994 [quant-ph]}, title = {Correlations constrained by composite measurements}, year = {2020}, month = sep, note = {arXiv: 2009.04994}, abstract = {How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations that physical theories may feature when restricted by some particular constraints on their measurements. We show that demanding that a theory exhibits a composite measurement imposes a hierarchy of constraints on the structure of its sets of states and effects, which translate to a hierarchy of constraints on the allowed correlations themselves. We moreover focus on the particular case where one demands the existence of an entangled measurement that reads out the parity of local fiducial measurements. By formulating a non-linear Optimisation Problem, and semidefinite relaxations of it, we explore the consequences of the existence of such a parity reading measurement for violations of Bell inequalities. In particular, we show that in certain situations this assumption has surprisingly strong consequences, namely, that Tsirelson's bound can be recovered.}, groups = {Michal_H}, keywords = {Quantum Physics}, url = {http://arxiv.org/abs/2009.04994}, urldate = {2021-07-28}, }`

- Siddhartha Das, Stefan Bäuml, Marek Winczewski, and Karol Horodecki. Universal limitations on quantum key distribution over a network.
*Arxiv:1912.03646 [quant-ph]*, sep 2020. arXiv: 1912.03646

[BibTeX] [Abstract] [Download PDF]

The possibility to achieve secure communication among trusted parties by means of the quantum entanglement is intriguing both from a fundamental and an application purpose. In this work, we show that any state (after distillation) from which a quantum secret key can be obtained by local measurements has to be genuinely multipartite entangled. We introduce the most general form of memoryless network quantum channel: quantum multiplex channels. We define and determine asymptotic and non-asymptotic LOCC assisted conference key agreement capacities for quantum multiplex channels and provide various strong and weak converse bounds in terms of the divergence based entanglement measures of the quantum multiplex channels. The structure of our protocol manifested by an adaptive strategy of secret key and entanglement (GHZ state) distillation over an arbitrary multiplex quantum channel is generic. In particular, it provides a universal framework to study the performance of quantum key repeaters and – for the first time – of the MDI-QKD setups of channels. For teleportation-covariant multiplex quantum channels, which are channels with certain symmetries, we get upper bounds on the secret key agreement capacities in terms of the entanglement measures of their Choi states. For some network prototypes of practical relevance, we evaluate upper bounds on the conference key agreement capacities and MDI-QKD capacities. Upper bounds on the LOCC-assisted conference key agreement rates are also upper bounds on the distillation rates of GHZ states, a class of genuinely entangled pure states. We also obtain bounds on the rates at which conference key and GHZ states can be distilled from a finite number of copies of an arbitrary multipartite quantum state. Using our bounds, in particular cases, we are able to determine the capacities for quantum key distribution channels and rates of GHZ-state distillation.

`@article{das_universal_2020, title = {Universal limitations on quantum key distribution over a network}, url = {http://arxiv.org/abs/1912.03646}, abstract = {The possibility to achieve secure communication among trusted parties by means of the quantum entanglement is intriguing both from a fundamental and an application purpose. In this work, we show that any state (after distillation) from which a quantum secret key can be obtained by local measurements has to be genuinely multipartite entangled. We introduce the most general form of memoryless network quantum channel: quantum multiplex channels. We define and determine asymptotic and non-asymptotic LOCC assisted conference key agreement capacities for quantum multiplex channels and provide various strong and weak converse bounds in terms of the divergence based entanglement measures of the quantum multiplex channels. The structure of our protocol manifested by an adaptive strategy of secret key and entanglement (GHZ state) distillation over an arbitrary multiplex quantum channel is generic. In particular, it provides a universal framework to study the performance of quantum key repeaters and - for the first time - of the MDI-QKD setups of channels. For teleportation-covariant multiplex quantum channels, which are channels with certain symmetries, we get upper bounds on the secret key agreement capacities in terms of the entanglement measures of their Choi states. For some network prototypes of practical relevance, we evaluate upper bounds on the conference key agreement capacities and MDI-QKD capacities. Upper bounds on the LOCC-assisted conference key agreement rates are also upper bounds on the distillation rates of GHZ states, a class of genuinely entangled pure states. We also obtain bounds on the rates at which conference key and GHZ states can be distilled from a finite number of copies of an arbitrary multipartite quantum state. Using our bounds, in particular cases, we are able to determine the capacities for quantum key distribution channels and rates of GHZ-state distillation.}, urldate = {2021-07-28}, journal = {arXiv:1912.03646 [quant-ph]}, author = {Das, Siddhartha and Bäuml, Stefan and Winczewski, Marek and Horodecki, Karol}, month = sep, year = {2020}, note = {arXiv: 1912.03646}, keywords = {Quantum Physics, Computer Science - Information Theory}, }`