Coherence measures with respect to general quantum measurements

TL;DR

This paper extends the concept of quantum coherence to general POVM measurements, introduces new measures, and proves a conjecture related to the $l_{1}$-norm coherence measure, enhancing understanding of quantum state advantages.

Contribution

It establishes an alternative framework for block coherence, introduces new POVM-based coherence measures, and proves a conjecture on the $l_{1}$-norm coherence measure.

Findings

Proposed several block coherence measures.

Developed coherence measures for POVM measurements.

Proved a conjecture on the $l_{1}$-norm POVM coherence measure.

Abstract

Quantum coherence with respect to orthonormal bases has been studied extensively in the past few years. Recently, Bischof, et al. [Phys. Rev. Lett. 123, 110402 (2019)] generalized it to the case of general positive operator-valued measure (POVM) measurements. Such POVM-based coherence, including the block coherence as a special case, have significant operational interpretations in quantifying the advantage of quantum states in quantum information processing. In this work we first establish an alternative framework for quantifying the block coherence and provide several block coherence measures. We then present several coherence measures with respect to POVM measurements, and prove a conjecture on the $l_{1}$-norm related POVM coherence measure.