Related papers: A characterization theorem for matrix variances
The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…
In a recent article, we gave a full characterization of matrices that can be decomposed as a linear combination of two idempotents with prescribed coefficients. In this one, we use those results to improve on a recent theorem of V.…
The necessary and sufficient condition of separability of a mixed state of any systems is presented, which is practical in judging the separability of a mixed state. This paper also presents a method of finding the disentangled…
We give sufficient conditions on a matrix A ensuring the existence of a partition of this matrix into two submatrices with extremely small norm of the image of any vector. Under some weak conditions on a matrix A we obtain a partition of A…
We consider the entire characteristic functions of order 2 and we prove some decomposition theorems in a multidimensional case. We show that the lack of zeros of the density function is a necessary but not a sufficient (as in the…
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
We present a partial characterization of matrices in $M_n(\cA)^+$ satisfying the St{\o}rmer condition.
The necessary and suffcient condition for a set of matrices to commute is given and proven.
We derive necessary and sufficient conditions for a group of density matrices to characterize what different people may know about one and the same physical system.
A minimal separating set is found for the algebra of matrix invariants of several 2x2 matrices over an infinite field of arbitrary characteristic
A necessary and sufficient condition for 1-distillability is formulated in terms of decomposable positive maps. As an application we provide insight into why all states violating the reduction criterion map are distillable and demonstrate…
A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent…
We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof.…
Understanding the behavior of a black-box model with probabilistic inputs can be based on the decomposition of a parameter of interest (e.g., its variance) into contributions attributed to each coalition of inputs (i.e., subsets of inputs).…
We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…
We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…
A new criterion is developed which provides a check as to whether a chosen set of polarization observables is complete with respect to the determination of all independent $T$-matrix elements of a reaction of the type $a+b\to c+d+...$. As…
We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We…