Related papers: Quantum Steering Ellipsoid Volume as a Measure on …
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…
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,…
The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a monogamy relation for the volumes of steering ellipsoids has been derived…
Any two-qubit state can be represented, geometrically, as an ellipsoid with a certain size and a center located within the Bloch sphere of one of the qubits. Points of this ellipsoid represent the post-measurement states when the other…
We propose a measure of quantum steerability, namely a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods…
The problem of of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices describing N--dimensional…
The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensional and 15-dimensional in nature, respectively. The total volumes of the spaces they occupy with respect to the Hilbert-Schmidt and Bures metrics are obtainable as…
Quantum steering ellipsoid visualizes the set of all qubit states that can be steered by measuring on another correlated qubit in the Bloch picture. Together with local reduced states, it provides a faithful geometric characterization of…
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…
According to the geometric characterization of measurement assemblages and local hidden state (LHS) models, we propose a steering criterion which is both necessary and sufficient for two-qubit states under arbitrary measurement sets. A…
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…
This note deals with estimating the volume of the set of separable mixed quantum states when the dimension of the state space grows to infinity. This has been studied recently for qubits; here we consider larger particles and conclude that,…
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 question of which two-qubit states are steerable (i.e. permit a demonstration of EPR-steering) remains open. Here, a strong necessary condition is obtained for the steerability of two-qubit states having maximally-mixed reduced states,…
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)…
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 show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric…
We introduce a measure of average dimensionality (or coherence) for high-dimensional quantum devices. This includes sets of quantum measurements, steering assemblages, and quantum channels. For measurements and channels, our measure…
We investigate the possibility of deriving analytical formulas for the 15-dimensional separable volumes, in terms of any of a number of metrics of interest (Hilbert-Schmidt [HS], Bures,...), of the two-qubit (four-level) systems. This would…
In the last few years, several criteria to identify Eistein-Podolski-Rosen steering have been proposed and experimentally implemented. On the operational side, however, the evaluation of the steerability degree of a given state has shown to…