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

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 [Formula: see text] 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 [Formula: see text] state mixed with white noise are given. They are compared with the sufficient condition for explicit full separability given in a previous work.