Related papers: Bloch Radii Repulsion in Separable Two-Qubit Syste…
We detect a certain pattern of behavior of separability probabilities $p(r_A,r_B)$ for two-qubit systems endowed with Hilbert-Schmidt, and more generally, random induced measures, where $r_A$ and $r_B$ are the Bloch radii ($0 \leq r_A,r_B…
Milz and Strunz ({\it J. Phys. A}: {\bf{48}} [2015] 035306) recently studied the probabilities that two-qubit and qubit-qutrit states, randomly generated with respect to Hilbert-Schmidt (Euclidean/flat) measure, are separable. They…
The geometric separability probability of composite quantum systems is extensively studied in the last decades. One of most simple but strikingly difficult problem is to compute the separability probability of qubit-qubit and rebit-rebit…
We first seek the rebit-retrit counterpart to the (formally proven by Lovas and Andai) two-rebit Hilbert-Schmidt separability probability of $\frac{29}{64} =\frac{29}{2^6} \approx 0.453125$ and the qubit-qutrit analogue of the (strongly…
A confluence of numerical and theoretical results leads us to conjecture that the Hilbert-Schmidt separability probabilities of the 15- and 9-dimensional convex sets of complex and real two-qubit states (representable by 4 x 4 density…
Firstly, we reduce the long-standing problem of ascertaining the Hilbert-Schmidt probability that a generic pair of qubits is separable to that of determining the specific nature of a one-dimensional (separability) function of the radial…
We employ a quasirandom methodology, recently developed by Martin Roberts, to estimate the separability probabilities, with respect to the Bures (minimal monotone/statistical distinguishability) measure, of generic two-qubit and two-rebit…
We conduct a pair of quasirandom estimations of the separability probabilities with respect to ten measures on the 15-dimensional convex set of two-qubit states, using its Euler-angle parameterization. The measures include the…
We begin by seeking the qubit-qutrit and rebit-retrit counterparts to the now well-established Hilbert-Schmidt separability probabilities for (the 15-dimensional convex set of) two-qubits of $\frac{8}{33} = \frac{2^3}{3 \cdot 11} \approx…
Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional…
Compelling evidence-though yet no formal proof-has been adduced that the probability that a generic (standard) two-qubit state ($\rho$) is separable/disentangled is $\frac{8}{33}$ (arXiv:1301.6617, arXiv:1109.2560, arXiv:0704.3723).…
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…
Employing Hilbert-Schmidt measure, we explicitly compute and analyze a number of determinantal product (bivariate) moments |rho|^k |rho^{PT}|^n, k,n=0,1,2,3,..., PT denoting partial transpose, for both generic (9-dimensional) two-rebit…
We extend the findings and analyses of our two recent studies (Phys. Rev. A, 75, 032326 [2007] and arXiv:0704.3723) by, first, obtaining numerical estimates of the separability function based on the (Euclidean, flat) Hilbert-Schmidt (HS)…
We seek to develop a Bures (minimal monotone/statistical distinguishability) metric-based series of formulas for the moments of probability distributions over the determinants $|\rho|$ and $|\rho^{PT}|$ of $4 \times 4$ density matrices,…
Previously, a formula, incorporating a $5F4$ hypergeometric function, for the Hilbert-Schmidt-averaged determinantal moments $\left\langle \left\vert \rho^{PT}\right\vert ^{n}\left\vert \rho\right\vert ^{k}\right\rangle /\left\langle…
We reexamine a recent analysis in which, using the volume of the associated quantum steering ellipsoid (QES) as a measure, we sought to estimate the probability that a two-qubit state is separable. In the estimation process, we, in effect,…
We list in increasing order -- 1/3, 3/8, 2/5, 135 pi/1024, 16/(3 pi^2), 3 pi/16, 5/8, 105 pi/512, 2 - 435 pi/1024, 11/16, 1 -- a number of exact two-qubit Hilbert-Schmidt (HS) separability probabilities, we are able to compute. Each…
We begin by investigating relationships between two forms of Hilbert-Schmidt two-re[al]bit and two-qubit "separability functions"--those recently advanced by Lovas and Andai (J. Phys. A 50 [2017] 295303), and those earlier presented by…
We report substantial progress in the study of separability functions and their application to the computation of separability probabilities for the real, complex and quaternionic qubit-qubit and qubit-qutrit systems. We expand our recent…