Detection and Classification of Three-qubit States Using $l_{1}$ Norm of Coherence

TL;DR

This paper introduces a method using the $l_{1}$ norm of coherence to detect and classify entanglement in three-qubit states, providing a way to identify genuine entanglement with specific criteria.

Contribution

The paper proposes a novel coherence-based criterion for detecting and classifying three-qubit entanglement, including a necessary condition to distinguish biseparable states.

Findings

The $l_{1}$ norm of coherence can identify entanglement in three-qubit states.

Violation of a certain condition indicates the state is not biseparable.

The method can conclusively determine genuine tripartite entanglement.

Abstract

Entanglement is a purely quantum mechanical phenomenon and thus it has no classical analog. On the other hand, coherence is a well-known phenomenon in classical optics and in quantum mechanics. Recent research shows that quantum coherence may act as a useful resource in quantum information theory. We will employ here quantum coherence to detect and classify the entanglement property of three-qubit states. Moreover, we have shown that if any three-qubit state violates another necessary condition for the detection of a general biseparable state then the given three-qubit state cannot be a biseparable state. Since there are only three categories of states for the three-qubit system so if we detect that the state under probe is neither a separable nor a biseparable state then we can definitely conclude that the given three-qubit state is a genuine entangled state. We have illustrated our results with a few examples.