Partial transposition on bi-partite system

Preprint English OPEN
Han, Y. -J. ; Ren, X. J. ; Wu, Y. C. ; Guo, G. -C. (2006)
  • Subject: Quantum Physics

Many of the properties of the partial transposition are not clear so far. Here the number of the negative eigenvalues of K(T)(the partial transposition of K) is considered carefully when K is a two-partite state. There are strong evidences to show that the number of negative eigenvalues of K(T) is N(N-1)/2 at most when K is a state in Hilbert space N*N. For the special case, 2*2 system(two qubits), we use this result to give a partial proof of the conjecture sqrt(K(T))(T)>=0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of K(T) or the negative entropy of K.
  • References (9)

    [1] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).

    [2] P. W. Shor, Proceedings 35th Annual symposium on foundations of computer science, (IEEE Press, Los Alamitos, CA, 1994).

    [3] L. K. Grover, Phys. Rev. Lett. 79, 325 (1997).

    [4] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, Phys. Rev. A. 54, 3824(1996).

    [5] V. Vedral and M. B. Plenio, Phys. Rev. A, 57, 1619 (1998).

    [6] V. Vedral, Rev. Mod. Phys. 74, 197 (2002).

    [7] M. Lewenstein, B. Kraus, J. I. Cirac and P. Horodecki, Phys. Rev. A 62, 052310 (2000).

    [8] M. Lewenstein, B. Kraus, J. I. Cirac and P. Horodecki, Phys. Rev. A 63, 044304 (2001).

    [9] W. Du¨r, J. I. Cirac and R. Tarrach, Phys. Rev. Lett. 83, 3562 (1999); W. Du¨r and J. I. Cirac, Phys. Rev. A 61, 042314 (2000);W. Du¨r and J. I. Cirac, Phys. Rev. A 62, 022302 (2000).

  • Metrics
    No metrics available
Share - Bookmark