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Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence. II--The Relevance of Dyson Indices | | Paul B. Slater
; | | Date: |
22 Oct 2008 | | Abstract: | We importantly amend a certain parenthetical remark made in Part I
(arXiv:0806.3294), to the effect that although two-qubit
diagonal-entry-parameterized separability functions had been shown
(arXiv:0704.3723) to clearly conform to a pattern dictated by the "Dyson
indices" (beta = 1 [real], 2 [complex], 4 [quaternionic]) of random matrix
theory, this did not appear to be the case with regard to
eigenvalue-parameterized separability functions (ESFs). But upon further
examination of the extensive numerical analyses reported in Part I, we find
quite convincing evidence that adherence to the Dyson-index pattern does also
hold for ESFs, at least as regards the upper half-range 1/2 <= C <= 1 of the
maximal concurrence over spectral orbits, C. To be specific, it strongly
appears that in this upper half-range, the real two-qubit ESF is simply
proportional to (2-2 C)^(3/2), and its complex counterpart--in conformity to
the Dyson-index pattern--proportional to the square of the real ESF, that is,
(2-2 C)^3. The previously documented piecewise continuous ("semilinear")
behavior in the lower half-range still appears, however, to lack any particular
Dyson-index-related interpretation. | | Source: | arXiv, 0810.3927 | | Services: | Forum | Review | PDF | Favorites | |
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