Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics

TL;DR

This paper links quantum Fisher information to the coherence cost in quantum thermodynamics, providing an operational interpretation and revealing a new connection between key quantum properties.

Contribution

It introduces a novel operational interpretation of quantum Fisher information as the coherence cost in state preparation without work restrictions.

Findings

Coherence cost is determined by quantum Fisher information.

Quantum Fisher information connects to fundamental quantum properties.

Provides a resource-theoretic framework for quantum thermodynamics.

Abstract

In the framework of quantum thermodynamics preparing a quantum system in a general state requires the consumption of two distinct resources, namely, work and coherence. It has been shown that the work cost of preparing a quantum state is determined by its free energy. Considering a similar setting, here we determine the coherence cost of preparing a general state when there are no restrictions on work consumption. More precisely, the coherence cost is defined as the minimum rate of consumption of systems in a pure coherent state, that is needed to prepare copies of the desired system. We show that the coherence cost of any system is determined by its quantum Fisher information about the time parameter, hence introducing a new operational interpretation of this central quantity of quantum metrology. Our resource-theoretic approach also reveals a previously unnoticed connection between two fundamental properties of quantum Fisher information.