Related papers: Decomposition and partial trace of positive matric…
We give an explicit description of the trace, or Hochschild homology, of the quantum Heisenberg category defined by Licata and Savage. We also show that as an algebra, it is isomorphic to "half" of a central extension of the elliptic Hall…
We study quantum processes, as one parameter families of differentiable completely positive and trace preserving (CPTP) maps. Using different representations of the generator, and the Sylvester criterion for positive semi-definite matrices,…
The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density…
When a projection of a symmetric or Hermitian matrix to the positive semidefinite cone is computed approximately (or to working precision on a computer), a natural question is to quantify its accuracy. A straightforward bound invoking…
We investigate the relationship between ideal membership of an operator and its pieces relative to several canonical types of partitions of the entries of its matrix representation with respect to a given orthonormal basis. Our main…
Basic properties of Uhlmann's partial fidelities are discussed. Statistical interpretation in terms of POVM measurements is established. Multiplicativity properties are considered. The relationship between partial fidelities and partitioned…
A proper set of indices characterizing the polarimetric purity of light and material media is defined from the eigenvalues of the corresponding coherency matrix. A simple and generalizable relation of these indices with the current…
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols are evaluated as normalized traces. This paper addresses…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
For a numerical semigroup ring $K[H]$ we study the trace of its canonical ideal. The colength of this ideal is called the residue of $H$. This invariant measures how far is $H$ from being symmetric, i.e. $K[H]$ from being a Gorenstein ring.…
Some variants of the (block) Gauss--Seidel iteration for the solution of linear systems with $M$-matrices in (block) Hessenberg form are discussed. Comparison results for the asymptotic convergence rate of some regular splittings are…
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 study integral operators on the space of square-integrable functions from a compact set, $X$, to a separable Hilbert space, $H$. The kernel of such an operator takes values in the ideal of Hilbert-Schmidt operators on $H$. We establish…
Almost-commuting matrices with respect to the normalized Hilbert-Schmidt norm are considered. Normal almost commuting matrices are proved to be near commuting.
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range of the off-diagonal block X, especially the distance from 0 to W(X).
The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected position observables in such systems. One expects the…
Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged on the energy shell, on the basis of independent particle Hamiltonians. One- and two-body matrix elements are compared with the quantal results and it is…
Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras to be generated by a set of…