# Converting Entanglement into Ensemble Basis-Free Coherence

## TL;DR

This paper explores how to convert quantum entanglement into coherence in ensembles of quantum states using measurement techniques.

## Contribution

The paper introduces two novel methods to generate ensemble coherence from entanglement using von Neumann measurements and symmetric observables.

## Key findings

- Applying von Neumann measurements to non-maximally entangled states can yield coherence equal to initial entanglement.
- Symmetric observables can generate ensembles useful in quantum key distribution protocols like B92 and BB84.

## 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—arising from the measurement–ensemble duality principle and the Born rule—connects the ensemble coherence with both the entanglement resource and the measurement’s uncertainty. This paper presents two methods for generating ensemble coherence from a fixed amount of entanglement between two qubit systems. 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.