Quantum Fluctuation Theorem under Continuous Measurement and Feedback

TL;DR

This paper derives a generalized quantum fluctuation theorem under continuous measurement and feedback, introducing a new quantum information measure called QC-transfer entropy, and verifies the theory through simulations and proposed experiments.

Contribution

It introduces QC-transfer entropy as a novel quantum information measure and derives the fluctuation theorem under continuous quantum feedback, linking quantum thermodynamics and information theory.

Findings

Derived the generalized fluctuation theorem for quantum systems with feedback

Introduced QC-transfer entropy as a new quantum information measure

Proposed experimental verification methods for the theoretical results

Abstract

While the fluctuation theorem in classical systems has been thoroughly generalized under various feedback control setups, an intriguing situation in quantum systems, namely under continuous feedback, remains to be investigated. In this work, we derive the generalized fluctuation theorem under continuous quantum measurement and feedback. The essence for the derivation is to newly introduce the operationally meaningful information, which we call quantum-classical-transfer (QC-transfer) entropy. QC-transfer entropy can be naturally interpreted as the quantum counterpart of transfer entropy that is commonly used in classical time series analysis. We also verify our theoretical results by numerical simulation and propose an experiment-numerics hybrid verification method. Our work reveals a fundamental connection between quantum thermodynamics and quantum information, which can be experimentally tested with artificial quantum systems such as circuit quantum electrodynamics.