Nonlocal advantage of quantum coherence in high-dimensional states

TL;DR

This paper extends the concept of nonlocal advantage of quantum coherence (NAQC) to high-dimensional states, providing criteria for detecting NAQC and entanglement, with potential applications in quantum information processing.

Contribution

The authors generalize NAQC criteria to $(d\times d)$-dimensional states where $d$ is a prime power, and establish a link between NAQC and quantum entanglement.

Findings

Derived criteria for NAQC in high-dimensional states.

Showed NAQC states are necessarily entangled.

Presented explicit examples demonstrating the framework's effectiveness.

Abstract

By local measurements on party $A$ of a system $AB$ and classical communication between its two parties, one can achieve a nonlocal advantage of quantum coherence (NAQC) on party $B$. For the $l_1$ norm of coherence and the relative entropy of coherence, we generalized the framework of NAQC for two qubits and derived the criteria which capture NAQC in the $(d\times d)$-dimensional states when $d$ is a power of a prime. We also presented a new framework for formulating NAQC, and showed through explicit examples its capacity on capturing the NAQC states. Moreover, we proved that any bipartite state with NAQC is quantum entangled, thus the obtained criteria can also be used as an entanglement witness.