摘要Many properties of partial transposition are unclear as yet. Here we carefully consider the number of the negative eigenvalues of ρT (ρ's partial transposition) when ρ is a two-partite state. There is strong evidence to show that the number of negative eigenvalues of ρT is N(N-1)/2 at most when ρ is a state in Hilbert space CN×CN. For the special case, the 2×2 system, we use this result to give a partial proof of the conjecture |ρT|T≥0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of ρ^T or the negative entropy of ρ.
Abstract：Many properties of partial transposition are unclear as yet. Here we carefully consider the number of the negative eigenvalues of ρT (ρ's partial transposition) when ρ is a two-partite state. There is strong evidence to show that the number of negative eigenvalues of ρT is N(N-1)/2 at most when ρ is a state in Hilbert space CN×CN. For the special case, the 2×2 system, we use this result to give a partial proof of the conjecture |ρT|T≥0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of ρ^T or the negative entropy of ρ.
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2008, Vol. 25 
