We study quantum dichotomies and the resource theory of asymmetric distinguishability using a generalization Strassen’s theorem on preordered semirings. find that an asymptotic variant relative submajorization, defined unnormalized dichotomies, is characterized by real-valued monotones are multiplicative under tensor product additive direct sum. These strong constraints allow us to classify exp...

This paper discusses the hazard rate order of fail-safe systems arising from two sets independent multiple-outlier scale distributed components. Under certain conditions on parameters in model and submajorization between sample size vectors, ordering corresponding random variables is established. Archimedean copula parameters, we also discuss usual stochastic these with dependent

Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n × n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give an spectral characterization of the set EA(Un(B)) = {EA(U B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit...

We note that the well-known result of Von Neumann \cite{von} is not valid for all doubly substochastic operators on discrete Lebesgue spaces $\ell^p(I)$, $p\in[1,\infty)$. This fact lead us to distinguish two classes these operators. Precisely, class increasable $\ell^p(I)$ isolated with property an analogue in this true. The submajorization relation $\prec_s$ positive cone $\ell^p(I)^+$, when ...

Let A be an n×n complex Hermitian matrix and let λ(A)=(λ1,…,λn)∈Rn denote the eigenvalues of A, counting multiplicities arranged in non-increasing order. Motivated by problems arising theory low rank approximation, we study spectral spread denoted Spr+(A), given Spr+(A)=(λ1−λn,λ2−λn−1,…,λk−λn−k+1)∈Rk, where k=[n/2] (integer part). The is a vector-valued measure dispersion spectrum that allows o...