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Biseparability of 3-qubits density matrices using Hilbert–Schmidt decompositions: Sufficient conditions and explicit expressions

Y. Ben-Aryeh

Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel

E-mail Address: phr65yb@physics.technion.ac.il

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and

A. Mann

Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel

E-mail Address: ady@physics.technion.ac.il

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https://doi.org/10.1142/S0219749916500441Cited by:4 (Source: Crossref)

Abstract

Hilbert–Schmidt (HS) decompositions and Frobenius norms are used to analyze biseparability of 3-qubit systems, with particular emphasis on density matrices with maximally disordered subsystems (MDS) and on the $W$ state mixed with white noise. The biseparable form of a MDS density matrix is obtained by using the Bell states of a 2-qubit subsystem, multiplied by density matrices of the third qubit, which include the relevant HS parameters. Using our methods, a sufficient condition and explicit biseparability of the $W$ state mixed with white noise are given. They are compared with the sufficient condition for explicit full separability given in a previous work.

Keywords:

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