Repository logo

Eventually entanglement breaking Markovian dynamics: structure and characteristic times

Published version

Change log


Hanson, Eric P 
Rouzé, Cambyse 
França, Daniel Stilck 


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 Poincar'e inequalities for nonprimitive semigroups to the discrete setting to quantify the convergence of quantum semigroups in discrete time, which is of independent interest.


Funder: Cantab Capital Institute for the Mathematics of Information


quant-ph, quant-ph

Journal Title

Annales Henri Poincaré

Conference Name

Journal ISSN


Volume Title



Springer Science and Business Media LLC