Related papers: Remarks on the Cross Norm Criterion for Separabili…
We revisit the application of different separability criteria by recourse to an exhaustive Monte Carlo exploration involving the pertinent state-space of pure and mixed states. The corresponding chain of implications of different criteria…
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it…
Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator.…
We propose a sufficient and necessary separability criterion for pure states in multipartite and high dimensional systems. Its main advantage is operational and computable. The obvious expressions of this criterion can be given out by the…
A family of separability criteria based on correlation matrix (tensor) is provided. Interestingly, it unifies several criteria known before like e.g. CCNR or realignment criterion, de Vicente criterion and derived recently separability…
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for…
In Ho, Russell, and Weiss, a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation $X=\ell_2$ and…
We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…
We propose the Linearly Adaptive Cross Entropy Loss function. This is a novel measure derived from the information theory. In comparison to the standard cross entropy loss function, the proposed one has an additional term that depends on…
Robustness to distribution shift and fairness have independently emerged as two important desiderata required of modern machine learning models. While these two desiderata seem related, the connection between them is often unclear in…
We analyze the separability properties of density operators supported on $\C^2\otimes \C^N$ whose partial transposes are positive operators. We show that if the rank of $\rho$ equals N then it is separable, and that bound entangled states…
Positivity of the density operator reflects itself in terms of sequences of inequalities on observable moments. Uncertainty relations for non-commuting observables form a subset of these inequalities. In addition, criterion of positivity…
The detection and estimation of quantum entanglement are the essential issues in the theory of quantum entanglement. We construct matrices based on the realignment of density matrices and the vectorization of the reduced density matrices,…
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…
Recent works have investigated the problem of the conflict redistribution in the fusion rules of evidence theories. As a consequence of these works, many new rules have been proposed. Now, there is not a clear theoretical criterion for a…
The aim of this note is twofold. Firstly, we prove an abstract version of the Calder\'on transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an operation does…
We investigate the Peres-Horodecki positive partial transpose (PPT) criterion in the context of conserved quantities and derive a condition of in- separability for a composite bipartite system depending only on the dimen- sions of its…
Causal continuity is usually defined by imposing the conditions (i) distinction and (ii) reflectivity. It is proved here that a new causality property which stays between weak distinction and causality, called feeble distinction, can…
A general and computable criterion for k-(in)separability in continuous multipartite quantum systems is presented. The criterion can be experimentally implemented with a finite and comparatively low number of local observables. We discuss…
We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. This framework enables us to express an indirect…