Quantum Jarzynski Equality with multiple measurement and feedback for isolated system

TL;DR

This paper extends the quantum Jarzynski equality to include cases with intermediate measurements and feedback control in isolated systems, highlighting how the equality is affected by measurement errors and information gain.

Contribution

It derives the quantum Jarzynski equality for isolated systems with intermediate measurements and feedback, incorporating classical measurement errors and mutual information effects.

Findings

JE remains unchanged with intermediate measurements without feedback.

JE is modified when feedback based on measurements is applied, involving mutual information.

The approach uses path probability in state space, differing from traditional density matrix methods.

Abstract

In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast to the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.