Predictive Complexity of Quantum Subsystems

Journal Article · 06 December 2024 · Entropy

DOI: https://doi.org/10.3390/e26121065 · OSTI ID:2480596

Asplund, Curtis T. ; Panciu, Elisa

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0024518
• OSTI ID: 2480596
• Journal Information: Entropy, Journal Name: Entropy Journal Issue: 12 Vol. 26; ISSN ENTRFG; ISSN 1099-4300
• Publisher: MDPI AGCopyright Statement
• Country of Publication: Switzerland
• Language: English