Physics – Quantum Physics
Scientific paper
2008-05-02
Journal of Geometry and Physics 59 (2009), pp. 17-31
Physics
Quantum Physics
30 pages, 7 figures, formula (48) for the Haar measure corrected by changing sin x_3 to sin^ x_3
Scientific paper
10.1016/j.geomphys.2008.08.008
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, can not be entangled by unitary transformations). In this regard, we make copious use of trigonometric identities involving the tetrahedral dihedral angle arccos(1/3).
Slater Paul B.
No associations
LandOfFree
Eigenvalues, Separability and Absolute Separability of Two-Qubit States does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Eigenvalues, Separability and Absolute Separability of Two-Qubit States, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Eigenvalues, Separability and Absolute Separability of Two-Qubit States will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-341641