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Volumn 67, Issue 2, 2003, Pages 12-

Maximal entanglement versus entropy for mixed quantum states

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EID: 85037212397     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.67.022110     Document Type: Article
Times cited : (66)

References (33)
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    • S. Lloyd, Science 261, 1589 (1993)
    • (1993) Science , vol.261 , pp. 1589
    • Lloyd, S.1
  • 5
    • 0029388979 scopus 로고
    • M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000)
    • ScienceD.P. DiVincenzo, 270, 255 (1995);M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
    • (1995) Science , vol.270 , pp. 255
    • DiVincenzo, D.P.1
  • 12
    • 85037211466 scopus 로고    scopus 로고
    • By entropy we mean a measure of how mixed a state is (i.e., its mixedness). We shall focus on two measures: the linear entropy and the von Neumann entropy, defined in Sec. III
    • By entropy we mean a measure of how mixed a state is (i.e., its mixedness). We shall focus on two measures: the linear entropy and the von Neumann entropy, defined in Sec. III.
  • 23
    • 85037208471 scopus 로고    scopus 로고
    • A separable (or unentangled) state (bipartite) (Formula presented) can be expressed as (Formula presented) whereas an entangled state has no such decomposition
    • A separable (or unentangled) state (bipartite) (Formula presented) can be expressed as (Formula presented) whereas an entangled state has no such decomposition.
  • 26
    • 85037230260 scopus 로고    scopus 로고
    • Suppose a bipartite density matrix (Formula presented) is expressed in the following form: (Formula presented) Then the partial transpose (Formula presented) of the density matrix (Formula presented) is defined via (Formula presented)We remark that the partial transpose depends on the basis chosen but the eigenvalues of the partially transposed matrix do not
    • Suppose a bipartite density matrix (Formula presented) is expressed in the following form: (Formula presented) Then the partial transpose (Formula presented) of the density matrix (Formula presented) is defined via (Formula presented)We remark that the partial transpose depends on the basis chosen but the eigenvalues of the partially transposed matrix do not.
  • 28
    • 85037221707 scopus 로고    scopus 로고
    • The main purpose for generating random states is to explore the boundary of the region, on the (Formula presented) versus (Formula presented) plane, of physically allowed states. The scheme by which we generate the eigenvalues of these states is, for the rank-4 case, as follows. We let (Formula presented) (Formula presented) (Formula presented) and (Formula presented) where (Formula presented) generates a random number in (Formula presented)
    • The main purpose for generating random states is to explore the boundary of the region, on the (Formula presented) versus (Formula presented) plane, of physically allowed states. The scheme by which we generate the eigenvalues of these states is, for the rank-4 case, as follows. We let (Formula presented) (Formula presented) (Formula presented) and (Formula presented) where (Formula presented) generates a random number in (Formula presented)


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