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Joint Hilbert-Schmidt Determinantal Moments for the Two-Rebit and Two-Qubit Systems | | Paul B. Slater
; | | Date: |
1 Apr 2011 | | Abstract: | We report formulas for the joint moments of the determinantal products
(det{rho})^k (det{rho^PT})^K (k=0, 1, 2,...,N; K = 0, 1, 2, 3, 4) of
Hilbert-Schmidt (HS) probability distributions over the two-rebit and (K = 0,
1) two-qubit density matrices rho. Here PT denotes the partial transposition
operation of quantum-information-theoretic importance. Each formula is the
product of the expression for the moments of (det{rho})^k,
k=0,1,2,...,N--already known from work of Cappellini, Sommers and Zyczkowski
(Phys. Rev. A 74, 062322 (1996))--and an adjustment factor. The factor is a
biproper rational function, with its numerators and denominators both being 3
K-degree polynomials in k. We infer the structure that the denominators follow
for arbitrary K. We hope to employ this extensive collection of moments to well
reconstruct the associated HS probabilities (for which we present plots) over
the two determinants, and to ascertain--at least to high accuracy--the
associated (separability) probabilities of "philosophical, practical and
physical" interest that (det{rho^PT})>0. | | Source: | arXiv, 1104.0217 | | Services: | Forum | Review | PDF | Favorites | |
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