Theory of Ergodic Quantum Processes
Theory of Ergodic Quantum Processes
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DOI：
10.1103/physrevx.11.041001
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发表时间：
2020-04
影响因子：
12.5
通讯作者：
R. Movassagh;Jeffrey Schenker
中科院分区：
文献类型：
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作者：
R. Movassagh;Jeffrey Schenker
长期以来，量子系统的类属行为一直是理论和实践关注的焦点。任何量子过程都可以用一系列量子通道来表示。随机信道出现在广泛的应用中，从量子混沌到量子引力理论中的全息对偶，再到算符动力学，再到随机局部电路，因为它们具有证明量子至上的潜力。我们考虑具有任意相关性和不可忽略的退相干的随机信道的一般遍历序列。遍历性包含并极大地推广了随机独立性。我们得到了一个定理，它表明这样的信道序列的合成以指数速度收敛到一阶(纠缠破缺)信道。在此基础上，我们得到了平移不变信道和随机独立随机信道的极限行为。然后，我们使用我们的形式来描述遍历矩阵乘积态的热力学极限。我们推导了局部能观量期望值的公式，并证明了局部能观量的两点关联是指数衰减的。然后，我们解析地计算了任意割线的纠缠谱，由此可以精确地计算任意割线的二体纠缠熵(即R{e}nyi或von Neumann)。我们的结果的其他物理含义是，大多数物质的Floquite相是亚稳态的，并且就其量子纠缠而言，大深度范围内的噪声随机电路将是微不足道的。为了得到这些结果，我们将量子信息理论与动力学系统和随机矩阵理论联系起来。
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. Random channels appear in a wide variety of applications, from quantum chaos to holographic dualities in theories of quantum gravity to operator dynamics, to random local circuits for their potential to demonstrate quantum supremacy. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity includes and vastly generalizes random independence. We obtain a theorem which shows that the composition of such a sequence of channels converges exponentially fast to a rank-one (entanglement breaking) channel. Using this, we derive the limiting behavior of translation invariant channels, and stochastically independent random channels. We then use our formalism to describe the thermodynamic limit of ergodic Matrix Product States. We derive formulas for the expectation value of a local observable and prove that the 2-point correlations of local observables decay exponentially. We then analytically compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy (i.e., R{e}nyi or von Neumann) across an arbitrary cut can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are meta-stable, and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned. To obtain these results we bridge quantum information theory to dynamical systems and random matrix theory.