Robustness of dynamical entropy

TL;DR

This paper investigates the robustness of dynamical entropy in quantum systems, showing that for certain models, the entropy measure remains stable under various measurement types, simplifying analysis.

Contribution

It demonstrates that in specific quantum models, dynamical entropy is robust against different measurement schemes, reducing the complexity of measurement choices.

Findings

Dynamical entropy remains stable under local measurements.

Von Neumann measurements suffice for quantum spin chains.

Gauge-invariant measurements are adequate for Fermion chains.

Abstract

When quantifying the mixing properties of a quantum dynamical system in terms of dynamical entropy, the following scheme appears natural: observe the state of the system at regular time intervals while it evolves and determine the entropy produced over time. It is clear that this entropy will not only depend on the type of dynamics, but also on the type of observations. Intuitively, one can expect that some measurements are better suited than others to reveal information about the dynamics, whereas many will generate undesirable noise. In this paper, we show for two widely used model systems that the dynamical entropy is rather robust in this respect. More precisely, general local positive operator-valued measurements may be restricted to von Neumann type measurements for the shift on a quantum spin chain and gauge-invariant ones for the shift on a Fermion chain.