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 \(\hbox {PPT}^2\) 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.

中文翻译：

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最终纠缠打破马尔可夫动力学：结构和特征时代

我们研究了离散和连续时间内马氏演化的纠缠破坏时间。在连续时间内，我们表征了哪些马尔可夫演化最终使纠缠破裂，即在一段有限的时间之后，最初存在的纠缠已被嘈杂的演化破坏了。在离散时间框架中，我们考虑纠缠破坏指数，即量子通道在变成纠缠破坏之前必须与自身组成的次数。的\（\ hbox中{PPT} ^ 2 \）推测每个PPT量子通道的纠缠破坏指数最大为2。我们证明每个忠实的PPT量子通道都有一个有限的纠缠破坏指数，更普遍的说，任何希尔伯特-施密特伴随物也是忠实的忠实的PPT CP映射最终都将发生纠缠破坏。我们还提供了一种方法，可以为任何忠实的量子通道获得该指标的具体界限。为了获得这些估计，我们使用了可分离性的鲁棒性的概念来获得忠实产品状态周围最大可分离球的半径范围。我们还将非本原半群的庞加莱不等式的框架扩展到离散集，以量化离散时间中量子半群的收敛，这是独立的利益。