相关论文: Exact Bures Probabilities that Two Quantum Bits ar…

Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon (quant-ph/9909044) have recently found necessary and sufficient conditions for the separability (classical correlation) of the Gaussian two-party (continuous…

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 consider a pair of one-parameter (alpha) families of generalized two-qubit determinantal Hilbert-Schmidt probability distributions, p_{alpha}(|rho^{PT}|) and q_{alpha}(|rho|), where rho is a 4 x 4 density matrix, rho^{PT}, its partial…

We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…

Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…

We study the interrelationships between the Fisher information metric recently introduced, on the basis of maximum entropy considerations, by Brody and Hughston (quant-ph/9906085) and the monotone metrics, as explicated by Petz and Sudar.…

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 notion of distance defined on the set of states of a composite quantum system can be used to quantify total, quantum and classical correlations in a unifying way. We provide new closed formulae for classical and total correlations 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…

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement…

The quantum information and the Bures metric are equivalent to each other, except at points where the rank of the density matrix changes. Here we show that by slightly modifying the definition of the Bures metric, the quantum information…

We report major advances in the research program initiated in "Moment-Based Evidence for Simple Rational-Valued Hilbert-Schmidt Generic 2 x 2 Separability Probabilities" (J. Phys. A, 45, 095305 [2012]). A highly succinct separability…

In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the…

The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical…

Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the Bures measure is proposed. This procedure may…

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 aim of this paper is to provide a method for explicit computation of the Bures metric over the space of $N$-level quantum system, based on the coset parametrization of density matrices.

The Bures metric is a natural choice in measuring the distance of density operators representing states in quantum mechanics. In the past few years a random matrix ensemble and the corresponding joint probability density function of its…

Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…

Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first…