Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements

TL;DR

This paper explores the relationship between quantum coherence and entanglement in quantum measurements, establishing resource theories and quantifying their conversion and interplay.

Contribution

It introduces a resource-theoretic framework linking quantum coherence and entanglement specifically for quantum measurements, including new quantifiers based on relative entropy.

Findings

Quantum coherence can be converted into entanglement in bipartite measurements.

Quantum entanglement monotones induce coherence monotones for measurements.

The link between coherence and entanglement holds even for resource-free measurements.

Abstract

Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this, we conceive a relative entropy type quantity to account for the quantum resources of quantum measurements. The quantum coherence of a quantum measurement can be converted into the entanglement in a bipartite quantum measurement through coherence-non generating transformations. Conversely, a quantum entanglement monotone of quantum measurements induces a quantum coherence monotone of quantum measurement. Our results confirm that the understanding on the link between quantum coherence and quantum entanglement is valid even for quantum measurements which do not generate any quantum resource.