论文标题
对角线正交协变量量子通道的厄法德理论
Ergodic theory of diagonal orthogonal covariant quantum channels
论文作者
论文摘要
我们分析了量子通道的千古特性，这些量子通道在对角线正交转换方面是协方差的。我们证明，该类别中通道的奇异行为基本上受经典随机矩阵的控制。这使我们能够利用经典的千古理论来研究此类渠道的量子性奇迹性。作为分析的应用，我们研究了双重统一电路，最近在多体系统中提出了量子混乱的最小模型。在这些电路上施加局部对角线正交不变性对称性后，在这种电路中局部可观察到的局部可观察物之间的长期行为完全取决于在对角线正交转化下协方差的通道的Ergodic特性。我们利用这一事实表明，这种对称双重统一电路表现出丰富的千古行为，从而强调了它们的重要性。
We analyze the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic matrix. This allows us to exploit tools from classical ergodic theory to study quantum ergodicity of such channels. As an application of our analysis, we study dual unitary brickwork circuits which have recently been proposed as minimal models of quantum chaos in many-body systems. Upon imposing a local diagonal orthogonal invariance symmetry on these circuits, the long-term behaviour of spatio-temporal correlations between local observables in such circuits is completely determined by the ergodic properties of a channel that is covariant under diagonal orthogonal transformations. We utilize this fact to show that such symmetric dual unitary circuits exhibit a rich variety of ergodic behaviours, thus emphasizing their importance.
