document: Frontier between separability and quantum entanglement in a many spin system We discuss the critical point x/sub c / separating the quantum entangled and separable states in two series of N spins S in the simple mixed state characterized by the matrix operator rho = x | phi > < phi | +1 - x/D/sup N/I/sub D/N , where x in -LSB- 0 , 1 -RSB- , D = 2S + 1 , I/sub D/N is the D/sup N / * D/sup N / unity matrix and | phi > is a special entangled state . The cases x = 0 and x = 1 correspond respectively to fully random spins and to a fully entangled state . In the first of these series we consider special states | phi > invariant under charge conjugation , that generalizes the N = 2 spin S = 1/2 Einstein-Podolsky-Rosen state , and in the second one we consider generalizations of the Werner -LRB- 1989 -RRB- density matrices . The evaluation of the critical point x/sub c / was done through bounds coming from the partial transposition method of Peres -LRB- 1996 -RRB- and the conditional nonextensive entropy criterion . Our results suggest the conjecture that whenever the bounds coming from both methods coincide the result of x/sub c / is the exact one . The results we present are relevant for the discussion of quantum computing , teleportation and cryptography
doc_bio_tags: O O B O B I O O B I I O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I I O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B O B
extractive_keyphrases: separability quantum entanglement many spin system separable states matrix operator unity matrix entangled state charge conjugation critical point partial transposition method nonextensive entropy criterion quantum computing teleportation cryptography
abstractive_keyphrases: random spin einstein-podolsky-rosen state werner density matrices