Eventually entanglement breaking Markovian dynamics: structure and characteristic times

Abstract

We investigate entanglement breaking times of Markovian evolutions in discrete and continuous time. In continuous time, we characterize which Markovian evolutions are eventually entanglement breaking, that is, evolutions for which there is a finite time after which any entanglement initially present has been destroyed by the noisy evolution. In the discrete time framework, we consider the entanglement breaking index, that is, the number of times a quantum channel has to be composed with itself before it becomes entanglement breaking. The PPT-square conjecture is that every PPT quantum channel has an entanglement breaking index of at most 2; we prove that every faithful PPT quantum channel has a finite entanglement breaking index, and more generally, any faithful PPT CP map whose Hilbert-Schmidt adjoint is also faithful is eventually entanglement breaking. We also provide a method to obtain concrete bounds on this index for any faithful quantum channel. To obtain these estimates, we use a notion of robustness of separability to obtain bounds on the radius of the largest separable ball around faithful product states. We also extend the framework of Poincaré inequalities for nonprimitive semigroups to the discrete setting to quantify the convergence of quantum semigroups in discrete time, which is of independent interest.

53 pages; accepted for publication in Annales Henri Poincaré

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• Positive maps and entanglement in real Hilbert spaces
• Continuity of quantum entropic quantities via almost convexity
• Asymptotics of quantum channels
• The PPT${}^2$ conjecture holds for all Choi-type maps
• Asymptotic Properties for Markovian Dynamics in Quantum Theory and General Probabilistic Theories
• Deviation bounds and concentration inequalities for quantum noises
• Asymptotic Dynamics of Open Quantum Systems and Modular Theory
• Random covariant quantum channels
• Separable Ball around any Full-Rank Multipartite Product State
• Separable ellipsoids around multipartite states
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps
• A triality pattern in entanglement theory
• A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
• Zero-error communication under discrete-time Markovian dynamics