Related papers: On independent permutation separability criteria

For years, independence has been considered as an important concept in many disciplines. Nevertheless, we present the first research that investigates the discovery problem of independence in data. In its arguably simplest form,…

We present an elementary and explicit proof of the separability criterion for continuous variable two-party Gaussian systems. Our proof is based on an elementary formulation of uncertainty relations and an explicit determination of…

We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…

We give a new separability criterion, a necessary condition for separability of $N$-partite quantum states. The criterion is based on the Bloch representation of a $N$-partite quantum state and makes use of multilinear algebra, in…

The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…

We consider the implications of the Revised Symmetrization Postulate (see quant-ph/9908078) for states of more than two particles. We show how to create permutation symmetric state vectors and how to derive alternative state vectors that…

We present combinatorial rules (one theorem and two conjectures) concerning three bases of Z[x1,x2,....]. First, we prove a "splitting" rule for the basis of key polynomials [Demazure '74], thereby establishing a new positivity theorem…

We present a generalized partial transposition separability criterion for the density matrix of a multipartite quantum system. This criterion comprises as special cases the famous Peres-Horodecki criterion and the recent realignment…

A decomposition form is introduced in this report to establish a criterion for the bi-partite separability of Bell diagonal states. A such criterion takes a quadratic form of the coefficients of a given Bell diagonal states and can be…

This paper introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating and testing the existence of mutually independent components for a given dataset, and a…

We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…

In this work, we explore Partitioned Independent Component Analysis (PICA), an extension of the well-established Independent Component Analysis (ICA) framework. Traditionally, ICA focuses on extracting a vector of independent source signals…

We derive necessary conditions in terms of the variances of position and momentum linear combinations for all kinds of separability of a multi-party multi-mode continuous-variable state. Their violations can be sufficient for genuine…

Inseparability criteria for continuous and discrete bipartite quantum states based on moments of annihilation and creation operators are studied by developing the idea of Shchukin-Vogel criterion [Phys. Rev. Lett. {\bf 95}, 230502 (2005)].…

A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive…

In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two of the involved permutations are long cycles, for which…

We derive criteria for $k$-separability of multipartite Quantum state

For any unitarily invariant convex function F on the states of a composite quantum system which isolates the trace there is a critical constant C such that F(w)<= C for a state w implies that w is not entangled; and for any possible D > C…

A very explicit analytic formula of the separability criterion of two-party Gaussian systems is given. This formula is compared to the past formulation of the separability criterion of continuous variables two-party Gaussian systems.

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…