Quantum inseparability as local pseudomixture

Abstract

We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a decomposition. Separable states correspond to mixing from one to four pure product states. Inseparable states can be described as pseudomixtures of four or five pure product states, and can be made separable by mixing them with one or two pure product states.

5 pages latex

References in corpus (4)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantifying Entanglement
• Separability criterion and inseparable mixed states with positive partial transposition
• Separability and entanglement of composite quantum systems

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