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Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps

2001; Elsevier BV; Volume: 283; Issue: 1-2 Linguagem: Inglês

10.1016/s0375-9601(01)00142-6

1873-2429

Michał Horodecki, Paweł Horodecki, Ryszard Horodecki,

Quantum Computing Algorithms and Architecture

We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of n−1 particles. The method of construction of the maps on the basis of unextendible product bases is provided. The three-qubit problem is discussed in more details involving Bloch sphere parameters of qubit state.