Seminars

The capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement. Analogous to entanglement, the notion of a causality measure characterizes the temporal aspect of quantum correlations. Despite holding an equally fundamental role in physics, temporal quantum correlations have yet to find their operational significance in quantum communication. Here we uncover a connection between quantum causality and channel capacity. We show the amount of temporal correlations between two ends of the noisy quantum channel, as quantified by a causality measure, implies a general upper bound on its channel capacity. The expression of this new bound is simpler to evaluate than most previously known bounds. We demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels, which results in improvement over previously known bounds for this class of channels.

Abstract of the paper: The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard’s engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory–bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.
Link to the paper: https://arxiv.org/abs/1806.00025

We study the classicality of a finite quantum system, called environment, defined by commutativity of the associate operator algebra, given sequential measurements on the environment. We demonstrate by constructing a scheme of probing from the pure-dephasing-type interaction with a qudit and preparation-evolution-measurement protocol thereon, the weak measurement sequence on the studied environment can be induced and some characteristics of the environment can be extracted from measurement statistics. From the general measurements on the environment, we consider its Kolmogorov consistency, the situation when a shorter length joint probability can be extracted from the longer one by summing the missing all possible intermediate outcomes. We provide general criteria for equivalence between Kolmogorov consistency of the statistics for arbitrary measurements and commutativity property of operator algebra of the environment, and apply the criteria to show explicitly for the induced measurements. As a result, we show that Kolmogorov consistency of the probability can be considered as a quantumness witness for its corresponding operator algebra of the environment if the conditional Hamiltonians are all non-degenerate. For the qubit, the equivalence can be obtained in general if one considers two axes of measurements namely X and Y.

As I will shortly move to ICTQT, in this talk I will try to give an overview of my work during the PhD. During this period I worked mainly on open quantum systems, applying collisional models to study both cascade systems (i.e. systems with a chiral propagation of information) and thermodynamic problems. On the other side, I also worked on potential engineering, that is, the design of potential profiles in order to obtain quantum states with specific properties or to perform specific tasks.

W roku 1984 Leroy i Blomme opracowali podstawy teoretyczne dyfrakcji dwóch spójnych wiązek światła na fali ultradźwiękowej padających na nią pod dodatnim i ujemnym kątem Bragga. W roku 2019 teoria Leroya i Blommego została potwierdzona eksperymentalnie. Dokonano tego korzystając z interferometru Macha-Zehndera, w którym zwierciadło wyjściowe interferometru zastąpiono falą ultradźwiękową. Otrzymano zgodnie z teorią Leroya-Blomego zdudnianie wychodzącego światła z interferometru z częstością fali ultradźwiękowej. Następnie zamiast wiązek światła wprowadzono do interferometru skorelowane pary fotonów. Na wyjściu z interferometru otrzymano dwufotonowe zdudnianie par fotonów z częstością równą podwójnej częstości fali ultradźwiękowej. W referacie zostaną przedstawione podstawy teoretyczne oraz otrzymane wyniki eksperymentalne teorii Leroya-Blomego oraz jedno i dwufotonowego zdudniania odpowiednio fotonów i par fotonów.

We show that the class MIP* of languages that can be decided by a classical verifier interacting with multiple all-powerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages. Our proof builds upon the quantum low-degree test of (Natarajan and Vidick, FOCS 2018) by integrating recent developments from (Natarajan and Wright, FOCS 2019) and combining them with the recursive compression framework of (Fitzsimons et al., STOC 2019). An immediate byproduct of our result is that there is an efficient reduction from the Halting Problem to the problem of deciding whether a two-player nonlocal game has entangled value 1 or at most 12. Using a known connection, undecidability of the entangled value implies a negative answer to Tsirelson’s problem: we show, by providing an explicit example, that the closure Cqa of the set of quantum tensor product correlations is strictly included in the set Cqc of quantum commuting correlations. Following work of (Fritz, Rev. Math. Phys. 2012) and (Junge et al., J. Math. Phys. 2011) our results provide a refutation of Connes’ embedding conjecture from the theory of von Neumann algebras

Link to the paper: https://arxiv.org/abs/2001.04383

A brief introduction to entanglement of multipartite pure quantum states will be given. As the Bell states are known to be maximally entangled among all two-qubit quantum states, a natural question arises: What is the most entangled state for the quantum system consisting of N sub-systems with d levels each? The answer depends on the entanglement measure selected, but already for four-qubit system there is no state, which displays maximal entanglement with respect to all three possible splittings of the systems into two pairs of qubits.
To construct strongly entangled multipartite quantum states one can use various mathematical techniques involving combinatorial designs, topological methods related to knot theory or the Majorana (stellar) representation of permutation symmetric quantum states. Absolutely maximally entangled (AME) states of 2n subsystems, being maximally entangled with respect to all possible symmetric splitting of the system, find their applications for information processing tasks. For instance, the standard |GHZ_4^3> state of four qutrits allows one to teleport a single qutrit between any two parties, while the ‘more entangled’ AME state of four qutrits enables us to teleport two qutrits from any selected pair of users to the remaining two parties.

Przedstawione będą argumenty sugerujące, że początek ewolucji biologicznej wymagał powstania prymitywnych silników chemicznych wytwarzających pracę w postaci mechanicznych oscylacji. Zasada działania takich silników byłaby podobna do funkcjonowania akumulatorów, baterii, a także ogniw paliwowych, fotowoltaicznych i termoelektrycznych. Zgodnie z rozwijaną przez autora i współpracowników teorią, wszystkie te urządzenia wykorzystują sprzężenie zwrotne prowadzące do autooscylacji elektrycznie naładowanej warstwy podwójnej.

In recent years, Solid State Nuclear Magnetic Resonance (NMR) has given us the chance to observe surprising dynamical emergent phenomena [1]. This is possible because this technique addresses spins in the thermodynamic limit. We have addressed two phenomena: A) the polarization a spin dimmer, may have a Rabi oscillation that becomes an overdamped polarization transfer when the interaction with a spin environment becomes enough strong as compared with the Rabi frequency [2]. B) A dipolar scaled dynamics [2], which is seen as an apparent spin-diffusion through the study of Out of Time Order Correlations (OTOCs) associated with collective polarization. However, when the Hamiltonian strength is weak respect to uncontrollable residual interactions, Loschmidt Echo experiments reveals that dynamical transition from a reversible dynamics to an irreversible one whose time constant is fixed by the Hamiltonian itself, not by the residual interactions. This intrinsic irreversibility, shows that one should be careful in applying the Schrödinger Equation to many-body systems in the thermodynamic limit.

[1]- Attenuation of polarization echoes in NMR: A test for the emergence of
Dynamical Irreversibility in Many-Body Quantum Systems. PR Levstein, G Usaj,
HM Pastawski; J. Chem. Phys. 108, 2718-2724 (1998)
[2]- Environmentally induced quantum dynamical phase transition in the spin
swapping operation. GA Álvarez, EP Danieli, PR Levstein, and HM Pastawski. J. Chem.
Phys. 124, 1 (2006)
[3]-Emergent perturbation independent decay of the Loschmidt echo in a many-body
system -Phys. Rev. Lett. (2020-in press) arXiv 1902.06628
CM Sánchez, AK Chattah, KX Wei, L Buljubasich, P Cappellaro, and HM Pastawski,
https://docs.google.com/document/d/1rJAySKRmj_iNXi6djMd6vZ4Bb3dNpVWrc3 OjIO6Rkw8/edit?usp=sharing [4]-Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and
emergent irreversibility, PR Zangara and HM Pastawski. Phys. Scr. 92 033001(2017)

The most general quantum object that can be shared between two distant parties is a bipartite quantum channel. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, for the first time we rigorously study the entanglement of bipartite channels. We follow a top-down approach, starting from general resource theories of processes, for which we present a new construction of a complete family of monotones, valid in all resource theories where the set of free superchannels is convex. In this setting, we define various general resource-theoretic protocols and resource monotones, which are then applied to the case of entanglement of bipartite channels. We focus in particular on the resource theory of NPT entanglement. Our definition of PPT superchannels allows us to express all resource protocols and monotones in terms of semi-definite programs. Along the way, we generalize the negativity measure to bipartite channels, and show that another monotone, the max-logarithmic negativity, has an operational interpretation as the exact asymptotic entanglement cost of a bipartite channel. Finally, we show that it is not possible to distill entanglement out of bipartite PPT channels under any set of free superchannels that can be used in entanglement theory, leading us in particular to the discovery of bound entangled POVMs.