An analytic approach to the problem of separability of quantum states based upon the theory of cones

作者：Salgado D^*; Sanchez Gomez J L; Ferrero M

来源：Quantum Information Processing, 2011, 10(5): 633-651.

DOI：10.1007/s11128-010-0223-9

• Entanglement
• Separability
• Cone
• Bipartite
• Multipartite

Exploiting the cone structure of the set of unnormalized mixed quantum states, we offer an approach to detect separability independently of the dimensions of the subsystems. We show that any mixed quantum state can be decomposed as rho = (1-lambda)C (rho) + lambda E (rho) , where C (rho) is a separable matrix whose rank equals that of rho and the rank of E (rho) is strictly lower than that of rho. With the simple choice times C-rho = M-1 circle times M-2 we have a necessary condition of separability in terms of lambda, which is also sufficient if the rank of E (rho) equals 1. We give a first extension of this result to detect genuine entanglement in multipartite states and show a natural connection between the multipartite separability problem and the classification of pure states under stochastic local operations and classical communication. We argue that this approach is not exhausted with the first simple choices included herein.

• 出版日期2011-10