Generalized coherence vector applied to coherence transformations and quantifiers

TL;DR

This paper introduces the generalized coherence vector in quantum coherence resource theory, providing a comprehensive characterization of quantum state conversions and proposing new coherence quantifiers based on this vector.

Contribution

It develops the generalized coherence vector, extending pure state coherence concepts to mixed states, and introduces a family of coherence quantifiers using this vector.

Findings

Generalized coherence vector fully characterizes incoherent and maximally coherent states.

Provides a necessary condition for quantum state conversion via incoherent operations.

Proposes new coherence quantifiers and compares them with existing measures.

Abstract

One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we advance on this characterization within the quantum coherence resource theory by introducing the generalized coherence vector of an arbitrary quantum state. The generalized coherence vector is a probability vector that can be interpreted as a concave roof extension of the pure states coherence vector. We show that it completely characterizes the notions of being incoherent, as well as being maximally coherent. Moreover, using this notion and the majorization relation, we obtain a necessary condition for the conversion of general quantum states by means of incoherent operations. These results generalize the necessary conditions of conversions for pure states given in the literature, and show that the tools of the majorization lattice are useful also in the general case. Finally, we introduce a family of coherence quantifiers by considering concave and symmetric functions applied to the generalized coherence vector. We compare this proposal with the convex roof measure of coherence and others quantifiers given in the literature.