The Fidelity and Trace Norm Distances for Quantifying Coherence

TL;DR

This paper examines fidelity and trace norm-based measures for quantum coherence, revealing limitations of fidelity and identifying conditions where trace norm effectively quantifies coherence.

Contribution

It demonstrates that fidelity-based coherence measures lack monotonicity and identifies trace norm as a valid coherence measure for specific quantum systems.

Findings

Fidelity of coherence does not satisfy monotonicity under subselection.

Trace norm of coherence is valid for qubits and certain qutrits.

Provides insights into coherence quantification methods.

Abstract

We investigate the coherence measures induced by fidelity and trace norm, based on the recent proposed coherence quantification in [Phys. Rev. Lett. 113, 140401, 2014]. We show that the fidelity of coherence does not in general satisfy the monotonicity requirement as a measure of coherence under the subselection of measurements condition. We find that the trace norm of coherence can act as a measure of coherence for qubit case and some special class of qutrits.