Basis-independent Coherence and its Applications

TL;DR

This paper introduces a basis-independent approach to quantum coherence, enabling analysis of coherence without basis dependence, and explores its connections to entanglement and discord with practical applications.

Contribution

It proposes a basis-independent definition of quantum coherence and compares it with traditional basis-dependent methods, highlighting advantages and applications.

Findings

Basis-independent coherence can be defined using invariant state sets.

The approach relates coherence to entanglement and discord via relative entropy.

Applications demonstrate the method's advantages over basis-dependent measures.

Abstract

In the quantitative theory of quantum coherence, the amount of coherence for given states can be meaningfully discussed only when referring to a preferred basis. One of the objections to this quantification is that the amount of coherence is an intrinsically basis-dependent quantity. This limitation can, however, be lifted when considering a set of quantum states invariant under arbitrary unitary transformations. Thus, we analyze a basis-independent definition of quantum coherence, and the incoherent state is taken as the maximally mixed state. We describe the relationship between the basis-independent and the basis-dependent approaches and give several applications to show the advantages of the former method. The relations among basis-independent coherence, quantum entanglement, and quantum discord are discussed by using the relative entropy within a multipartite system.