کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1898817 | 1044785 | 2009 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Eigenvalues, separability and absolute separability of two-qubit states
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Eigenvalues, separability and absolute separability of two-qubit states Eigenvalues, separability and absolute separability of two-qubit states](/preview/png/1898817.png)
چکیده انگلیسی
Substantial progress has recently been reported in the determination of the Hilbert-Schmidt (HS) separability probabilities for two-qubit and qubit-qutrit (real, complex and quaternionic) systems. An important theoretical concept employed has been that of a separability function. It appears that if one could analogously obtain separability functions parameterized by the eigenvalues of the density matrices in question-rather than the diagonal entries, as originally used-comparable progress could be achieved in obtaining separability probabilities based on the broad, interesting class of monotone metrics (the Bures, being its most prominent [minimal] member). Though large-scale numerical estimations of such eigenvalue-parameterized functions have been undertaken, it seems desirable also to study them in lower-dimensional specialized scenarios in which they can be exactly obtained. In this regard, we employ an Euler-angle parameterization of SO(4) derived by S. Cacciatori (reported in an Appendix)-in the manner of the SU(4)-density-matrix parameterization of Tilma, Byrd and Sudarshan. We are, thus, able to find simple exact separability (inverse-sine-like) functions for two real two-qubit (rebit) systems, both having three free eigenvalues and one free Euler angle. We also employ the important Verstraete-Audenaert-de Moor bound to obtain exact HS probabilities that a generic two-qubit state is absolutely separable (that is, cannot be entangled by unitary transformations). In this regard, we make copious use of trigonometric identities involving the tetrahedral dihedral angle Ï=cosâ1(13).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 59, Issue 1, January 2009, Pages 17-31
Journal: Journal of Geometry and Physics - Volume 59, Issue 1, January 2009, Pages 17-31
نویسندگان
Paul B. Slater,