Coherence measures based on sandwiched R\'{e}nyi relative entropy

TL;DR

This paper introduces two new classes of quantum coherence measures based on sandwiched Rényi relative entropy within the established BCP framework, and analyzes their properties and limitations.

Contribution

It proposes novel coherence measures based on sandwiched Rényi relative entropy and examines their characteristics, including the constraints on deriving new measures from existing ones.

Findings

Two classes of coherence measures are introduced.

New measures are consistent with the BCP framework.

Limitations on generating new measures from existing ones are identified.

Abstract

Coherence is a fundamental ingredient for quantum physics and a key resource for quantum information theory. Baumgratz, Cramer, and Plenio established a rigorous framework (BCP framework) for quantifying coherence [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. \textbf{113}, 140401 (2014)]. In this paper, under the BCP framework we provide two classes of coherence measures based on the sandwiched R\'{e}nyi relative entropy. We also prove that we can not get new coherence measures $f(C(\cdot))$ by a function $f$ acting on a given coherence measure $C$, except the case of qubit states.