Related papers: Decomposition and partial trace of positive matric…
We give a criterion for H-convergence of conductivity matrices in terms of ordinary weak convergence of the factors in certain quotient representations of the matrices.
Given a positive noncommutative polynomial $f$, equivalently a sum of Hermitian squares (SOHS), there exists a positive semidefinite Gram matrix that encrypts all the structural essence of $f$. There are no available methods for extending a…
A symmetric tensor, which has a symmetric nonnegative decomposition, is called a completely positive tensor. We consider the completely positive tensor decomposition problem. A semidefinite algorithm is presented for checking whether a…
For any finite reductive group, we compute the central elements in its Hecke algebra that arise from partial Springer resolutions via the Harish-Chandra transform. Of the two kinds of partial resolution, the larger is the more interesting…
In this note we give a brief survey of the most elementary criteria used to determine the surjectivity of the trace operator on the ring of integers of a number field $K$. Furthermore, we introduce an easy to state yet unknown surjectivity…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
We propose a purely algebraic approach to construct invariants of transversal links in the standard contact structure on the 3-sphere generalizing Jones' approach to invariant of usual links. The only geometry used is the analogue of…
The positive and not completely positive maps of density matrices, which are contractive maps, are discussed as elements of a semigroup. A new kind of positive map (the purification map), which is nonlinear map, is introduced. The density…
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…
A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…
We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis.…
Conjugate partial-symmetric (CPS) tensor is a generalization of Hermitian matrices. For the CPS tensor decomposition some properties are presented. For real CPS tensors in particular, we note the subtle difference from the complex case of…
We bring in some new notions associated with $2\times 2$ block positive semidefinite matrices. These notions concern the inequalities between the singular values of the off diagonal blocks and the eigenvalues of the arithmetic mean or…
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable, c) completely positive, d) extended by identity impose…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
State, trace, and moment polynomials are polynomial expressions in several operator or random variables and positive functionals on their products (states, traces or expectations). While these concepts, and in particular their positivity…
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…
We derive the large distance asymptotics of the Fredholm determinant of the so-called generalised sine kernel at the critical point. This kernel corresponds to a generalisation of the pure sine kernel arising in the theory of random…
A partial matrix is a matrix where only some of the entries are given. We determine the maximum rank of the symmetric completions of a symmetric partial matrix where only the diagonal blocks are given and the minimum rank and the maximum…