On PPT States in C^K ○×C^M ○×C^N Composite Quantum Systems

We study the general representations of positive partial transpose (PPT) states in CK CM CN. For the PPT states with rank-N a canonical form is obtained, from which a sufficient separability condition is presented.

Separability of Rank—Two Quantum States in C^M ×CN Composite Quantum Systems

We consider rank-two density matrices ρ supported on an M × N Hilbert space for arbitrary dimensions M and N. Explicit sufficient and necessary conditions for separability of ρ are presented.

Canonical Form, and Separability of PPT States in C^2×C^2×C^2×C^N Composite Quantum Systems

We give a canonical form of PPT states in C2(×)C2(×)C2(×)CN with rank = N. From this canonical form a sufficient separability condition for these states is presented.