All entangled states are quantum coherent with locally distinguishable bases

TL;DR

This paper establishes a fundamental link between entanglement and quantum coherence, showing that entangled states are precisely those that exhibit local distinguishability-based coherence, with implications for understanding quantum correlations.

Contribution

It demonstrates that bipartite entanglement is equivalent to quantum coherence relative to locally distinguishable bases, connecting coherence measures to entanglement quantification.

Findings

Entangled states are exactly those coherent in locally distinguishable bases.

Minimal quantum coherence equals the entanglement of formation.

Connections established between coherence, entanglement, and their relative entropy measures.

Abstract

We find that a bipartite quantum state is entangled if and only if it is quantum coherent with respect to complete bases of states in the corresponding system that are distinguishable under local quantum operations and classical communication. The corresponding minimal quantum coherence is the entanglement of formation. Connections to the relative entropy of entanglement and quantum coherence, and generalizations to the multiparty case are also considered.