Predictive complexity of quantum subsystems

TL;DR

This paper introduces a quantum generalization of predictive complexity for subsystems, which better captures dynamic events and entanglement properties than traditional entanglement entropy, with applications demonstrated in spin chain models.

Contribution

It defines quantum predictive states and complexity, extending entanglement entropy, and shows their effectiveness in analyzing quantum dynamics and entanglement structures.

Findings

Predictive complexity better indicates dynamic events like magnon collisions.

It can distinguish long-range from short-range entanglement.

Demonstrated in isotropic Heisenberg spin chain models.

Abstract

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.