TY - JOUR

T1 - Eventually Entanglement Breaking Markovian Dynamics

T2 - Structure and Characteristic Times

AU - Hanson, Eric P.

AU - Rouzé, Cambyse

AU - Stilck França, Daniel

PY - 2020

Y1 - 2020

N2 - 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 2 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 non-primitive semigroups to the discrete setting to quantify the convergence of quantum semigroups in discrete time, which is of independent interest.

AB - 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 2 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 non-primitive semigroups to the discrete setting to quantify the convergence of quantum semigroups in discrete time, which is of independent interest.

UR - http://www.scopus.com/inward/record.url?scp=85081725279&partnerID=8YFLogxK

U2 - 10.1007/s00023-020-00906-4

DO - 10.1007/s00023-020-00906-4

M3 - Journal article

AN - SCOPUS:85081725279

VL - 21

SP - 1517

EP - 1571

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

IS - 5

ER -