隐量子马尔可夫模型和多体状态的非自适应读出
Hidden Quantum Markov Models and non-adaptive read-out of many-body states
摘要：
随机有限状态发生器是无限时间序列的压缩描述。或者，压缩描述由量子有限态生成器给出[K. Wiesner和J.P.Crutchfield，Physica D 237，1173（2008）]。这些都是基于对量子动力学系统的重复冯诺依曼测量。在这里，我们推广的量子有限态生成器取代冯诺依曼投影随机量子操作。通过这种方式，我们保证任何具有随机压缩描述的时间序列都具有压缩的量子描述。此外，我们建立了我们的随机发电机和顺序读出的多体状态与几何不变矩阵产品状态表示之间的联系。作为一个例子，我们考虑非自适应读出的1D集群状态。这被证明是等效于一个隐藏的量子模型与两个内部状态，提供洞察的内在复杂性的过程。最后，通过实例证明了量子描述比经典随机描述具有更高的压缩度。
英文摘要：
Stochastic finite-state generators are compressed descriptions of infinite time series. Alternatively, compressed descriptions are given by quantum finite- state generators [K. Wiesner and J. P. Crutchfield, Physica D 237, 1173 (2008)]. These are based on repeated von Neumann measurements on a quantum dynamical system. Here we generalise the quantum finite-state generators by replacing the von Neumann pro jections by stochastic quantum operations. In this way we assure that any time series with a stochastic compressed description has a compressed quantum description. Moreover, we establish a link between our stochastic generators and the sequential readout of many-body states with translationally-invariant matrix product state representations. As an example, we consider the non-adaptive read-out of 1D cluster states. This is shown to be equivalent to a Hidden Quantum Model with two internal states, providing insight on the inherent complexity of the process. Finally, it is proven by example that the quantum description can have a higher degree of compression than the classical stochastic one.
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