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Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States

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  • Paul B. Slater
  • Charles F. Dunkl

Abstract

Previously, a formula, incorporating a hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments of density-matrices ( ) and their partial transposes ( ), was applied with to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities ( ) are found— via a high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit ( ), (standard) two-qubit ( ), and two-quater[nionic]bit ( ) cases. We deduce rather simple companion (rebit, qubit, quaterbit, …) formulas that successfully reproduce the rational values assumed for general . These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula.

Suggested Citation

  • Paul B. Slater & Charles F. Dunkl, 2015. "Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-9, May.
    • Handle: RePEc:hin:jnlamp:621353
    DOI: 10.1155/2015/621353
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