Relating the Resource Theories of Entanglement and Quantum Coherence

TL;DR

This paper unifies the resource theories of quantum entanglement and coherence, analyzing their interplay in state formation and distillation under local incoherent operations and classical communication, and introduces new measures and criteria.

Contribution

It introduces a new framework linking entanglement and coherence resource theories, with a monotone for bipartite coherence distillation and refined distillability criteria.

Findings

Identifies minimum coherence-entanglement resources for pure states.

Introduces a new LIOCC monotone for bipartite coherence distillation.

Shows a bipartite mixed state has distillable entanglement iff it can be distilled by LIOCC.

Abstract

Quantum coherence and quantum entanglement represent two fundamental features of non-classical systems that can each be characterized within an operational resource theory. In this paper, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a given state, and we introduce a new LIOCC monotone that completely characterizes a state's optimal rate of bipartite coherence distillation. This result allows us to precisely quantify the difference in operational powers between global incoherent operations, LIOCC, and local incoherent operations \textit{without} classical communication. Finally, a bipartite mixed state is shown to have distillable entanglement if and only if entanglement can be distilled by LIOCC, and we strengthen the well-known Horodecki criterion for distillability.