Coherence based inequality for the discrimination of three-qubit GHZ and W class

TL;DR

This paper establishes a fundamental relationship between quantum coherence and entanglement, introduces a coherence-based inequality for classifying three-qubit states, and discusses potential experimental implementations.

Contribution

It derives a hierarchy between coherence and concurrence and introduces a coherence-based inequality for distinguishing GHZ and W class states.

Findings

The l1-norm of coherence is always greater than concurrence.

A monogamy inequality based on partial coherence is established.

A coherence-based criterion classifies GHZ and W states.

Abstract

Quantum coherence and entanglement orignate from the superposition principle. We derive a rigorous relation between the ${l_1}$-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherence based inequality for the classification of GHZ class and W class of three-qubit states. Finally, we provide theoretical discussion for the possible implementation of the scheme in an experiment.