Related papers: Numerical Computations of Separability Probabiliti…
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…
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
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…
The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria…
We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested, and…
We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…
After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…
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…
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 ({\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…
We present a family of 3--qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for…
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…
The probability that a generic real, complex or quaternionic two-qubit state is separable can be considered to be the sum of three contributions. One is from those states that are absolutely separable, that is those (which can not be…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…
The separability and entanglement of quantum mixed states in $\Cb^2 \otimes \Cb^3 \otimes \Cb^N$ composite quantum systems are investigated. It is shown that all quantum states $\rho$ with positive partial transposes and rank $r(\rho)\leq…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random…
We present separability criteria for both bipartite and multipartite quantum states. These criteria include the criteria based on the correlation matrix and its generalized form as special cases. We show by detailed examples that our…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…