Incomplete measurement of work in a dissipative two level system

TL;DR

This paper investigates the effects of incomplete photon measurements on the fluctuation relations in a quantum two-level system coupled to thermal baths, proposing a correction method using mutual information and discussing experimental prospects.

Contribution

It introduces a framework to recover fluctuation relations under partial measurement conditions in quantum systems, incorporating mutual information to account for unobserved photon exchanges.

Findings

Partial measurements cause deviations from standard fluctuation relations.

Mutual information can be used to correct these deviations.

Experimental calorimetric measurement with near single-photon sensitivity is feasible.

Abstract

We discuss work performed on a quantum two-level system coupled to multiple thermal baths. To evaluate the work, a measurement of photon exchange between the system and the baths is envisioned. In a realistic scenario, some photons remain unrecorded as they are exchanged with baths that are not accessible to the measurement, and thus only partial information on work and heat is available. The incompleteness of the measurement leads to substantial deviations from standard fluctuation relations. We propose a recovery of these relations, based on including the mutual information given by the counting efficiency of the partial measurement. We further present the experimental status of a possible implementation of the proposed scheme, i.e. a calorimetric measurement of work, currently with nearly single-photon sensitivity.