Strong and weak separability conditions for two-qubits density matrices

TL;DR

This paper derives explicit conditions for the separability of two-qubit mixed states, distinguishing between strong and weak separability, and provides necessary and sufficient criteria for these states.

Contribution

It introduces a clear distinction between strong and weak separability and establishes necessary and sufficient conditions for the separability of two-qubit density matrices.

Findings

Derived explicit separability conditions for two-qubit states

Defined strong and weak separability based on density matrix factorizations

Identified when two-qubit states are strongly separable under these conditions

Abstract

Explicit separable density matrices, for mixed two qubits states, are derived by the use of Hilbert Schmidt decompositions and Peres Horodecki criterion. A strongly separable two qubits mixed state is defined by multiplications of two density matrices given with pure states while weakly separable two qubits state is defined by multiplications of two density matrices which includes non-pure states. We find the sufficient and necessary condition for separability of two-qubits density matrices and show that under this condition the two-qubit density matrices are strongly separable.