Analysis on the von Neumann entropy under the measurement-based feedback control

TL;DR

This paper investigates how the von Neumann entropy of a quantum system behaves under measurement-based feedback control, deriving conditions for its non-decrease and illustrating with a qubit stabilization example.

Contribution

It provides a rigorous condition linking entropy change to observable variance and decoherence, advancing understanding of entropy dynamics in quantum feedback control.

Findings

Derived a sufficient condition for nonnegative entropy derivative under MBF

Linked entropy behavior to observable variance and decoherence

Validated results through a qubit stabilization example

Abstract

The measurement-based feedback (MBF) control offers several powerful means for preparing the desired target quantum state. Therefore, it is important to investigate fundamental properties of MBF. In particular, how the entropy of the controlled system under the MBF behaves is of great interest. In this study, we examine this problem by deriving a sufficient condition that the time derivative of the von Neumann entropy is nonnegative under the MBF control. This result is rigorously characterized by the variance of the system observable and the quantumness of a given decoherence. We show the validity of the result and physical interpretation in the example of qubit stabilizing.