Related papers: Eigenvalues, Separability and Absolute Separabilit…
We pursue a number of analytical directions, motivated to some extent initially by the possibility of developing a methodology for formally proving or disproving a certain conjecture of quantum-theoretical relevance (quant-ph/0308037). It…
Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…
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…
Separability from the spectrum is a significant and ongoing research topic in quantum entanglement. In this study, we investigate properties related to absolute separability from the spectrum in qudits-qudits states in the bipartite states…
A method allowing to increase a computational efficiency of evaluation of non-local characteristics of a pair of qubits is described. The method is based on the construction of coordinates on a generic section of 2-qubit's entanglement…
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…
We investigate the geometric characterization of pure state bipartite entanglement of $(2\times{D})$- and $(3\times{D})$-dimensional composite quantum systems. To this aim, we analyze the relationship between states and their images under…
An important variable in the 2017 analysis of Lovas and Andai, formally establishing the Hilbert-Schmidt separability probability conjectured by Slater of $\frac{29}{64}$ for the 9-dimensional convex set of two-rebit density matrices, was…
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…
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…
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…
Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By…
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 treat 3-qubits states with maximally disordered subsystems, by using Hilbert-Schmidt decompositions.By using unfolding methods, the tensors are converted into matrices and by applying singular values decompositions to these matrices the…
A conceptually simpler proof of the separability criterion for two-qubit systems, which is referred to as "Hefei inequality" in literature, is presented. This inequality gives a necessary and sufficient separability criterion for any mixed…
The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states {\rho} with the property that U^*{\rho}U is separable for all unitary matrices U. This problem has been solved when the…
We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the…
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…
For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.
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…