Acta Polytechnica

A note on entanglement classification for tripartite mixed states

Hui Zhao, Yu-Qiu Liu, Zhi‐Xi Wang, Shao-Ming Fei

Published Feb 28, 2022• 0 citations

Abstract

We study the classification of entanglement in tripartite systems by using Bell-type inequalities and principal basis. By using Bell unctions and the generalized three dimensional Pauli operators, we present a set of Bell inequalities which classifies the entanglement of triqutrit fully separable and bi-separable mixed states. By using the correlation tensors in the principal basis representation of density matrices, we obtain separability criteria for fully separable and bi-separable 2 ⊗ 2 ⊗ 3 quantum mixed states. Detailed example is given to illustrate our criteria in classifying the tripartite entanglement.

DOI: 10.14311/ap.2022.62.0222

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Acta Polytechnica

A note on entanglement classification for tripartite mixed states

Hui Zhao, Yu-Qiu Liu, Zhi‐Xi Wang, Shao-Ming Fei

Published Feb 28, 2022• 0 citations

Publisher

Abstract

DOI: 10.14311/ap.2022.62.0222

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The classification of the multipartite entanglement is an important problem in quantum information theory. We propose a class of two qubit mixed states

σ_{AB}= p|χ_{1}\rangle\langleχ_{1}|\otimesρ_{1}+(1-p)|χ_{2}\rangle\langleχ_{2}|\otimesρ_{2}

, where

|χ_{1}\rangle=α|0\rangle+β|1\rangle

|χ_{2}\rangle=β|0\rangle+(-1)^{n}α|1\rangle

. We have shown that the state

σ_{AB}

represent a classical state when

n

is odd while it represent a non-classical state when

n

is even. The purification of the state

σ_{AB}

is studied and found that the purification is possible if the spectral decomposition of the density matrices

ρ_{1}

and

ρ_{2}

represent pure states. We have established a relationship between three tangle, which measures the amount of entanglement in three qubit system and the quantity

\langleχ_{1}|χ_{2}\rangle

, which identifies whether the two qubit mixed state is classical or non-classical. The three qubit purified state is then classified as a separable or biseparable or W-type or GHZ-type state using the quantum correlation, measured by geometric discord, of its reduced two qubit density matrix.