Identification of three-qubit entanglement

TL;DR

This paper introduces a comprehensive method for identifying various types of entanglement in three-qubit states using expectation values of Pauli operators and inequalities for mixed states, aiding experimental detection.

Contribution

It provides explicit necessary and sufficient conditions for classifying three-qubit pure states and proposes inequalities for mixed states, enhancing entanglement detection techniques.

Findings

Explicit conditions for classifying three-qubit pure states.

Two inequalities for detecting entanglement in mixed states.

Effective method for experimental entanglement identification.

Abstract

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.