Converting entanglement into ensemble basis-free coherence

TL;DR

This paper explores how entanglement can be converted into basis-free coherence in quantum ensembles, introducing two methods that relate initial entanglement to resulting coherence, with implications for quantum key distribution protocols.

Contribution

It presents two novel methods for generating ensemble coherence from fixed entanglement, linking entanglement to basis-free coherence in quantum ensembles.

Findings

Coherence can equal initial entanglement using von Neumann measurements.

Symmetric observables can generate ensembles for QKD protocols.

The work enhances understanding of entanglement-to-coherence conversion.

Abstract

The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of quantum states remain an area of active research. The entanglement-based approach to ensemble coherence - where a partial measurement of an entangled state generates an ensemble - relates the ensemble coherence to both the initial entanglement and the measurement's uncertainty. This paper presents two methods for generating ensemble coherence from a fixed amount of entanglement. The first method involves applying a von Neumann measurement to one part of a non-maximally entangled bipartite state, resulting in a pair of non-orthogonal states whose coherence can equal the initial entanglement. The second method considers a class of symmetric observables capable of generating ensembles used in quantum key distribution (QKD) protocols such as B92, BB84, and three-state QKD. As a result, this work contributes to understanding how much ensemble coherence can be obtained from a given amount of entanglement.