Quantum Coherence: A Fundamental Resource for Establishing Genuine Multipartite Correlations

TL;DR

This paper reveals a fundamental link between quantum coherence and genuine multipartite entanglement, showing that coherence can generate entanglement and correlates with steering and nonlocality in multi-qubit systems.

Contribution

It establishes an exact equivalence between measures of genuine multipartite entanglement and coherence, and explores their relationship with quantum steering and nonlocality.

Findings

Genuine multipartite entanglement measures are equivalent to coherence measures via convex roof.

Genuine multipartite steering and nonlocality occur if and only if coherence is present in the state.

Coherence can be used to generate genuine multipartite entanglement through incoherent operations.

Abstract

We establish the profound equivalence between measures of genuine multipartite entanglement(GME) and their corresponding coherence measures. Initially we construct two distinct classes of measures for genuine multipartite entanglement utilizing real symmetric concave functions and the convex roof technique. We then demonstrate that all coherence measures for any qudit states, defined through the convex roof approach, are identical to our two classes of GME measures of the states combined with an incoherent ancilla under a unitary incoherent operation. This relationship implies that genuine multipartite entanglement can be generated from the coherence inherent in an initial state through the unitary incoherent operations. Furthermore, we explore the interplay between coherence and other forms of genuine quantum correlations, specifically genuine multipartite steering and genuine multipartite nonlocality. In the instance of special three-qubit X-states (only nonzero elements of X-state are diagonal or antidiagonal when written in an orthonormal basis), we find that genuine multipartite steering and nonlocality are present if and only if the coherence exists in the corresponding qubit states.