Seminars

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.

A number of noncontextual models exist which reproduce different subsets of quantum theory and admit a no-cloning theorem. Therefore, if one chooses noncontextuality as one’s notion of classicality, no-cloning cannot be regarded as a nonclassical phenomenon. In this work, however, we show that there are aspects of the phenomenology of quantum state cloning which are indeed nonclassical according to this principle. Specifically, we focus on the task of state-dependent cloning and prove that the optimal cloning fidelity predicted by quantum theory cannot be explained by any noncontextual model. We derive a noise-robust noncontextuality inequality whose violation by quantum theory not only implies a quantum advantage for the task of state-dependent cloning relative to noncontextual models, but also provides an experimental witness of noncontextuality.

The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras.We define the asymmetry of an operator with respect to an algebraic basis in terms of their commutators. Detailed analysis is given to the Lie algebra SU(2) and its q-deformation. The asymmetry of the q-deformed integrable spin chain models is calculated. The corresponding geometrical pictures with respect to such asymmetry is presented.

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.