Asplund Curtis T, Panciu Elisa
Department of Physics & Astronomy, San José State University, One Washington Square, San José, CA 95192-0106, USA.
Department of Physics, University of Maryland, College Park, MD 20742-4111, USA.
Entropy (Basel). 2024 Dec 7;26(12):1065. doi: 10.3390/e26121065.
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement.
我们为由不同子系统组成的量子系统定义了预测状态和预测复杂度。这种复杂度是纠缠熵的一种推广。它的灵感来源于随机和复杂系统理论中预测状态分析的统计或预测复杂度，但本质上是量子的。子系统的预测状态由外部希尔伯特空间中状态向量的等价类形成，这些等价类在一段时间内有效地预测该子系统的相同未来行为。作为一个示例，我们给出了各向同性海森堡模型自旋链动力学的计算，并表明，与纠缠熵相比，预测复杂度能更好地表示动态重要事件，比如磁振子碰撞。它还可以作为一个局域序参量，用于区分长程和短程纠缠。
