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Dyson-Index-Like Behavior of Bures Separability Function | | Paul B. Slater
; | | Date: |
30 Aug 2007 | | Abstract: | We conduct a study based on the Bures (minimal monotone) metric, analogous to
that recently reported for the Hilbert-Schmidt (flat or Euclidean) metric
(arXiv:0704.3723v2). Among the interesting results obtained there had been
proportionalities--in exact correspondence to the Dyson indices eta = 1, 2, 4
of random matrix theory--between the fourth, second and first powers of the
separability functions S_{type}(mu) for real, complex and quaternionic
qubit-qubit scenarios, Here mu=sqrt{frac{
ho_{11}
ho_{44}}{
ho_{22}
ho_{33}}}, with
ho being a 4 x 4 density matrix. Separability functions
have proved useful--in the framework of the Bloore (correlation
coefficient/off-diagonal scaling) parameterization of density matrices--for the
calculation of separability probabilities. We find--for certain, basic simple
scenarios (in which the diagonal entries of
ho are unrestricted, and one or
two off-diagonal [real, complex or quaternionic] pairs of entries are nonzero)
--that these proportionalities no longer strictly hold in the Bures case, but
do come remarkably close to holding. | | Source: | arXiv, 0708.4208 | | Services: | Forum | Review | PDF | Favorites | |
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