##### Leader of the research group: Ana Belen Sainz

Post-docs: Marcin Karczewski, David Schmid

PhD students: Paulo Cavalcanti, Vinicius Pretti Rossi, Beata Zjawin

The broad aim of the Foundational Underpinnings of Quantum Technologies Group is to understand the quantum manifestation of nonclassical phenomena, and how harness such nonclassicality for information processing. This is tackled from a novel perspective, combining an operational vision with the process-theoretic framework.

## Activity

Specific goals of the group include:

– Formulate candidate theories that supersede quantum. In particular, explore which possible

deviations of quantum theory are still sensible.

– Study causality within and beyond quantum theory, from a process-theoretic perspective.

– Characterise the quantum manifestation of nonclassical phenomena. The main focus will be on Bell nonlocality, contextuality, steering, and correlations in causal networks.

– Develop resource theories to address quantification.

– Identify current and new forms of nonclassicality as resources for quantum technologies.

– Assess nonclassical speed-up for computation, within and beyond quantum theory.

– Contribute to the development of a systematic approach to quantum program optimisation based on the zx-calculus, by further developing the foundations of the latter.

## Publications

### 2020

- Paul Skrzypczyk, Matty J. Hoban, Ana Belén Sainz, and Noah Linden. Complexity of compatible measurements.
*Physical Review Research*, 2(2):23292, jun 2020. doi:10.1103/PhysRevResearch.2.023292

[BibTeX] [Download PDF]`@Article{skrzypczyk_complexity_2020, author = {Skrzypczyk, Paul and Hoban, Matty J. and Sainz, Ana Belén and Linden, Noah}, journal = {Physical {R}eview {R}esearch}, title = {Complexity of compatible measurements}, year = {2020}, issn = {2643-1564}, month = jun, number = {2}, pages = {023292}, volume = {2}, doi = {10.1103/PhysRevResearch.2.023292}, language = {en}, url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.023292}, urldate = {2020-06-24}, }`

- Ana Belén Sainz, Matty J. Hoban, Paul Skrzypczyk, and Leandro Aolita. Bipartite Postquantum Steering in Generalized Scenarios.
*Physical Review Letters*, 125(5):50404, jul 2020. doi:10.1103/PhysRevLett.125.050404

[BibTeX] [Download PDF]`@Article{sainz_bipartite_2020, author = {Sainz, Ana Belén and Hoban, Matty J. and Skrzypczyk, Paul and Aolita, Leandro}, journal = {Physical {R}eview {L}etters}, title = {Bipartite {Postquantum} {Steering} in {Generalized} {Scenarios}}, year = {2020}, issn = {0031-9007, 1079-7114}, month = jul, number = {5}, pages = {050404}, volume = {125}, doi = {10.1103/PhysRevLett.125.050404}, language = {en}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.050404}, urldate = {2021-05-10}, }`

- Sandu Popescu, Ana Belén Sainz, Anthony J. Short, and Andreas Winter. Reference Frames Which Separately Store Noncommuting Conserved Quantities.
*Physical Review Letters*, 125(9):90601, aug 2020. doi:10.1103/PhysRevLett.125.090601

[BibTeX] [Download PDF]`@Article{popescu_reference_2020, author = {Popescu, Sandu and Sainz, Ana Belén and Short, Anthony J. and Winter, Andreas}, journal = {Physical {R}eview {L}etters}, title = {Reference {Frames} {Which} {Separately} {Store} {Noncommuting} {Conserved} {Quantities}}, year = {2020}, issn = {0031-9007, 1079-7114}, month = aug, number = {9}, pages = {090601}, volume = {125}, doi = {10.1103/PhysRevLett.125.090601}, language = {en}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.090601}, urldate = {2021-05-10}, }`

- Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens. Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes.
*Quantum*, 4:280, jun 2020. doi:10.22331/q-2020-06-08-280

[BibTeX] [Abstract] [Download PDF]

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular causal structure, namely, one wherein the wings are only connected by a common cause. We term them “common-cause boxes”. We define the distinction between classical and nonclassical resources in terms of whether or not a classical causal model can explain the correlations. One can then quantify the relative nonclassicality of resources by considering their interconvertibility relative to the set of operations that can be implemented using a classical common cause (which correspond to local operations and shared randomness). We prove that the set of free operations forms a polytope, which in turn allows us to derive an efficient algorithm for deciding whether one resource can be converted to another. We moreover define two distinct monotones with simple closed-form expressions in the two-party binary-setting binary-outcome scenario, and use these to reveal various properties of the pre-order of resources, including a lower bound on the cardinality of any complete set of monotones. In particular, we show that the information contained in the degrees of violation of facet-defining Bell inequalities is not sufficient for quantifying nonclassicality, even though it is sufficient for witnessing nonclassicality. Finally, we show that the continuous set of convexly extremal quantumly realizable correlations are all at the top of the pre-order of quantumly realizable correlations. In addition to providing new insights on Bell nonclassicality, our work also sets the stage for quantifying nonclassicality in more general causal networks.

`@article{wolfe_quantifying_2020, title = {Quantifying {Bell}: the {Resource} {Theory} of {Nonclassicality} of {Common}-{Cause} {Boxes}}, volume = {4}, issn = {2521-327X}, shorttitle = {Quantifying {Bell}}, url = {https://quantum-journal.org/papers/q-2020-06-08-280/}, doi = {10.22331/q-2020-06-08-280}, abstract = {We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular causal structure, namely, one wherein the wings are only connected by a common cause. We term them "common-cause boxes". We define the distinction between classical and nonclassical resources in terms of whether or not a classical causal model can explain the correlations. One can then quantify the relative nonclassicality of resources by considering their interconvertibility relative to the set of operations that can be implemented using a classical common cause (which correspond to local operations and shared randomness). We prove that the set of free operations forms a polytope, which in turn allows us to derive an efficient algorithm for deciding whether one resource can be converted to another. We moreover define two distinct monotones with simple closed-form expressions in the two-party binary-setting binary-outcome scenario, and use these to reveal various properties of the pre-order of resources, including a lower bound on the cardinality of any complete set of monotones. In particular, we show that the information contained in the degrees of violation of facet-defining Bell inequalities is not sufficient for quantifying nonclassicality, even though it is sufficient for witnessing nonclassicality. Finally, we show that the continuous set of convexly extremal quantumly realizable correlations are all at the top of the pre-order of quantumly realizable correlations. In addition to providing new insights on Bell nonclassicality, our work also sets the stage for quantifying nonclassicality in more general causal networks.}, language = {en}, urldate = {2021-05-10}, journal = {Quantum}, author = {Wolfe, Elie and Schmid, David and Sainz, Ana Belén and Kunjwal, Ravi and Spekkens, Robert W.}, month = jun, year = {2020}, pages = {280}, }`

### 2019

- Thomas Van Himbeeck, Jonatan Bohr Brask, Stefano Pironio, Ravishankar Ramanathan, Ana Belén Sainz, and Elie Wolfe. Quantum violations in the Instrumental scenario and their relations to the Bell scenario.
*Quantum*, 3:186, 2019. doi:10.22331/q-2019-09-16-186

[BibTeX] [Abstract] [Download PDF]

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.

`@Article{van_himbeeck_quantum_2019, author = {Van Himbeeck, Thomas and Bohr Brask, Jonatan and Pironio, Stefano and Ramanathan, Ravishankar and Sainz, Ana Belén and Wolfe, Elie}, journal = {Quantum}, title = {Quantum violations in the {Instrumental} scenario and their relations to the {Bell} scenario}, year = {2019}, issn = {2521-327X}, month = sep, pages = {186}, volume = {3}, abstract = {The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.}, doi = {10.22331/q-2019-09-16-186}, groups = {Belen}, language = {en}, url = {https://quantum-journal.org/papers/q-2019-09-16-186/}, urldate = {2020-04-22}, }`

## 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}, }`

- 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}, }`

- David Schmid, Thomas C. Fraser, Ravi Kunjwal, Ana Belen Sainz, Elie Wolfe, and Robert W. Spekkens. Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory.
*Arxiv:2004.09194 [quant-ph]*, may 2021. arXiv: 2004.09194

[BibTeX] [Abstract] [Download PDF]

A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., entanglement, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.

`@article{schmid_understanding_2021, title = {Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory}, shorttitle = {Understanding the interplay of entanglement and nonlocality}, url = {http://arxiv.org/abs/2004.09194}, abstract = {A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., entanglement, then the common assumption is that the appropriate choice of free operations is Local Operations and Classical Communication (LOCC). We here advocate for the study of a different choice of free operations, namely, Local Operations and Shared Randomness (LOSR), and demonstrate its utility in understanding the interplay between the entanglement of states and the nonlocality of the correlations in Bell experiments. Specifically, we show that the LOSR paradigm (i) provides a resolution of the anomalies of nonlocality, wherein partially entangled states exhibit more nonlocality than maximally entangled states, (ii) entails new notions of genuine multipartite entanglement and nonlocality that are free of the pathological features of the conventional notions, and (iii) makes possible a resource-theoretic account of the self-testing of entangled states which generalizes and simplifies prior results. Along the way, we derive some fundamental results concerning the necessary and sufficient conditions for convertibility between pure entangled states under LOSR and highlight some of their consequences, such as the impossibility of catalysis for bipartite pure states. The resource-theoretic perspective also clarifies why it is neither surprising nor problematic that there are mixed entangled states which do not violate any Bell inequality. Our results motivate the study of LOSR-entanglement as a new branch of entanglement theory.}, urldate = {2021-07-28}, journal = {arXiv:2004.09194 [quant-ph]}, author = {Schmid, David and Fraser, Thomas C. and Kunjwal, Ravi and Sainz, Ana Belen and Wolfe, Elie and Spekkens, Robert W.}, month = may, year = {2021}, note = {arXiv: 2004.09194}, keywords = {Quantum Physics}, }`

- 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}, }`

### 2020

- 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}, }`

## Group members

###### Get to know the people behind ICTQT.

## Former members

#### Victoria J Wright

__Keywords:__ quantum nonlocality, quantum contextuality, steering, causality, Bell’s theorem, process theories, generalised probabilistic theories, quantum computational speedup, quantum networks, resource theories, post-quantum theories, post-quantum nonclassicality, zx-calculus.