Related papers: Bures and Hilbert-Schmidt 2 x 2 Determinantal Mome…

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…

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…

In a number of previous studies, we have investigated the use of the volume element of the Bures (minimal monotone) metric -- identically, one-fourth of the statistical distinguishability (SD) metric -- as a natural measure over the…

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…

Hubner's formula for the Bures (statistical distance) metric is applied to both a one-parameter and a two-parameter series (n=2,...,7) of sets of 2^n x 2^n density matrices. In the doubly-parameterized series, the sets are comprised of the…

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 derive the probability--expressed in terms of the Hilbert-Schmidt (Euclidean or flat) metric--that a generic (nine-dimensional) real two-qubit system is separable, by implementing the well-known Peres-Horodecki test on the…

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…

Compelling evidence-though yet no formal proof--has been adduced that the probability that a generic two-qubit state ($\rho$) is separable is $\frac{8}{33}$ (arXiv:1301.6617, arXiv:1109.2560, arXiv:0704.3723). Proceeding in related…

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 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 conduct a study based on the Bures (minimal monotone) metric, analogous to that recently reported for the Hilbert-Schmidt (flat or Euclidean) metric (arXiv:0704.3723v2). Among the interesting results obtained there had been…

We find equivalent hypergeometric- and difference-equation-based formulas, $Q(k,\alpha)= G_1^k(\alpha) G_2^k(\alpha)$, for $k = -1, 0, 1,\ldots,9$, for that (rational-valued) portion of the total separability probability for generalized…

We implement a procedure-based on the Wishart-Laguerre distribution-recently outlined by {\.Z}yczkowski and Khvedelidze, Rogojin and Abgaryan, for the generation of random (complex or real) $N \times N$ density matrices of rank $k \leq N$…

Two-qubit X-matrices have been the subject of considerable recent attention, as they lend themselves more readily to analytical investigations than two-qubit density matrices of arbitrary nature. Here, we maximally exploit this relative…

We report a concise answer--in the case of 2 x 2 systems--to the fundamental quantum-information-theoretic question as to "the volume of separable states" posed by Zyczkowski, Horodecki, Sanpera and Lewenstein (Phys. Rev. A, 58, 883…

Jakobczyk and Siennicki studied two-dimensional sections of a set of (generalized) Bloch vectors corresponding to n x n density matrices of two-qubit systems (that is, the case n = 4). They found essentially five different types of…

To begin, we find certain formulas $Q(k,\alpha)= G_1^k(\alpha) G_2^k(\alpha)$, for $k = -1, 0, 1,...,9$. These yield that part of the total separability probability, $P(k,\alpha)$, for generalized (real, complex, quaternionic,\ldots)…

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…