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

TL;DR

This paper develops criteria using Hilbert-Schmidt decompositions to determine biseparability of 3-qubit density matrices, providing explicit conditions and expressions especially for states with maximally disordered subsystems and noisy W states.

Contribution

It introduces new sufficient conditions and explicit formulas for biseparability of 3-qubit states using HS decompositions, advancing understanding of quantum state separability.

Findings

Derived a sufficient condition for biseparability of MDS states

Provided explicit biseparability expressions for W states with white noise

Compared biseparability criteria with full separability conditions

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.