Related papers: On maps which preserve semipositivity and quantifi…
This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.
We characterize all linear operators on finite or infinite-dimensional spaces of univariate real polynomials preserving the sets of elliptic, positive, and non-negative polynomials, respectively. This is done by means of Fischer-Fock…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
Elimination of quantifiers is shown to fail dramatically for a group of well-known mathematical theories (classically enjoying the property) against a wide range of relevant logical backgrounds. Furthermore, it is suggested that only by…
The question of whether given density operators for subsystems of a multipartite quantum system are compatible to one common total density operator is known as the quantum marginal problem. We briefly review the solution of a subclass of…
The Quantum Fisher Information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we…
Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings and $\varphi: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re$ has a nontrivial idempotents. Under certain…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity…
In this work, we investigate quantum Fisher information(QFI) and quantum coherence(QC) of an atom in dissipative cavity. In zero temperature reservior and with one excitation number, we obtain the analytical solutions of QFI and QC as well…
Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints. We prove that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim(PVP)…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
A problem of completing a linear map on C*-algebras to a completely positive map is analyzed. It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some…
A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is found that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both…
Denote $\Sigma_n$ and $Q_n$ the set of all $n \times n$ symmetric and skew-symmetric matrices over a field $\mathbb{F}$, respectively, where $char(\mathbb{F})\neq 2$ and $\lvert \mathbb{F} \rvert \geq n^2+1$. A characterization of…
We study the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. The post-processing order is fundamental as it enables to compare measurements by their intrinsic noise and it…
We show that positivity on $\mathbb{R}_+^n$ and on $\mathbb{R}^n$ of real symmetric polynomials of degree at most $p$ in $n\ge2$ variables is solvable by algorithms running in $\mathrm{poly}(n)$ time. For real symmetric quartics, we find…
We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results…
This article provides sufficient conditions for positive maps on the Schatten classes $\mathcal J_{p}, 1\le p<\infty$ of bounded operators on a separable Hilbert space such that a corresponding Perron-Frobenius theorem holds. With…
Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…