Partial coherence and quantum correlation with fidelity and affinity distances

TL;DR

This paper introduces a unified framework using fidelity and affinity distances to quantify quantum resources like entanglement and coherence, linking partial coherence to quantum discrimination and correlation measures.

Contribution

It establishes that fidelity and affinity distances satisfy strong contractibility, enabling resource quantification across various quantum resource theories, and connects partial coherence to quantum state discrimination.

Findings

Fidelity and affinity distances satisfy strong contractibility.

Fidelity partial coherence equals minimal error probability in quantum state discrimination.

Partial coherence measures quantum correlations in bipartite states.

Abstract

A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding resource quantifiers can be used to characterize a large class of resource theories. Under two assumptions, namely, convexity of "free states" and closure of free states under "selective free operations", our general framework of resource theory includes quantum resource theories of entanglement, coherence, partial coherence and superposition. In partial coherence theory, we show that fidelity partial coherence of a bipartite state is equal to the minimal error probability of a mixed quantum state discrimination (QSD) task and vice versa, which complements the main result in [Xiong and Wu, J. Phys. A: Math. Theor. 51, 414005 (2018)]. We also compute the analytic expression of fidelity partial coherence for $(2,n)$ bipartite X-states. At last, we study the correlated coherence in the framework of partial coherence theory. We show that partial coherence of a bipartite state, with respect to the eigenbasis of a subsystem, is actually a measure of quantum correlation.