Related papers: Quasirandom estimations of two-qubit operator-mono…
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…
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…
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,…
In a previous study (quant-ph/0207181), we formulated a conjecture that arbitrarily coupled qubits (describable by 4 x 4 density matrices) are separable with an a priori probability of 8/(11 \pi^2) = 0.0736881. For this purpose, we employed…
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 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…
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…
We study, further, a conjectured formula for generalized two-qubit Hilbert-Schmidt separability probabilities that has recently been proven by Lovas and Andai (https://arxiv.org/pdf/1610.01410.pdf) for its real (two-rebit) asserted value…
In a previous study (quant-ph/9911058), several remarkably simple exact results were found, in certain specialized m-dimensional scenarios (m<5), for the a priori probability that a pair of qubits is unentangled/separable. The measure used…
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 ($0 \leq r_A,r_B…
We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs…
We extend the findings and analyses of our two recent studies (Phys. Rev. A, 75, 032326 [2007] and arXiv:0704.3723) by, first, obtaining numerical estimates of the separability function based on the (Euclidean, flat) Hilbert-Schmidt (HS)…
The geometric separability probability of composite quantum systems is extensively studied in the last decades. One of most simple but strikingly difficult problem is to compute the separability probability of qubit-qubit and rebit-rebit…
Compelling evidence-though yet no formal proof-has been adduced that the probability that a generic (standard) two-qubit state ($\rho$) is separable/disentangled is $\frac{8}{33}$ (arXiv:1301.6617, arXiv:1109.2560, arXiv:0704.3723).…
Employing the volume of quantum steering ellipsoids (QSEs) as a measure on the fifteen-dimensional convex set of two-qubit states, we estimate the ratio of the integral of the measure over the separable states to its integral over all…
Paralleling our recent computationally-intensive (quasi-Monte Carlo) work for the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041)…
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…
Extensive numerical integration results lead us to conjecture that the silver mean, that is, s = \sqrt{2}-1 = .414214 plays a fundamental role in certain geometries (those given by monotone metrics) imposable on the 15-dimensional convex…
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…
Milz and Strunz recently reported substantial evidence to further support the previously conjectured separability probability of $\frac{8}{33}$ for two-qubit systems ($\rho$) endowed with Hilbert-Schmidt measure. Additionally, they found…