Related papers: Equality condition for a matrix inequality by part…

For a class of linear maps on a von Neumann factor, we associate two objects, bounded operators and trace class operators, both of which play the roles of Choi matrices. Each of them is positive if and only if the original map on the factor…

Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement…

We formulate the accuracy of quantum measurement for a qubit system in terms of a 3 by 3 matrix. This matrix, which we refer to as the accuracy matrix, can be calculated from a positive operator-valued measure (POVM) corresponding to the…

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…

We propose an information-theoretic framework for matrix completion. The theory goes beyond the low-rank structure and applies to general matrices of "low description complexity". Specifically, we consider $m\times n$ random matrices…

We study the martingale problem associated with the operator $L u = \partial_s u + 1/2 \sum_{i,j=1}^{d_0} a^{ij} \partial_{ij} u + \sum_{i,j=1}^d B^{ij} x^j \partial_i u$, where $d_0 \leq d$. We show that the martingale problem is…

In a scenario where two parties share, act on and exchange some physical resource, the assumption that the parties' actions are ordered according to a definite causal structure yields constraints on the possible correlations that can be…

In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result…

Computing $p \rightarrow q$ norm for matrices is a classical problem in computational mathematics and power iteration is a well-known method for computing $p \rightarrow q $ norm for a matrix with nonnegative entries. Here we define an…

It is well known that if $A\in\mathbb{C}^{N\times N}$ and $B\in\mathbb{C}^{N\times M}$ form a controllable pair (in the sense that the Kalman matrix $[B\ |\ AB\ | \ \dots\ |\ A^{N-1}B]$ has full rank) then, there exists…

We prove that every infinite sequence of skew-symmetric or symmetric matrices M_1, M_2, ... over a fixed finite field must have a pair M_i, M_j (i<j) such that M_i is isomorphic to a principal submatrix of the Schur complement of a…

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…

The problem of finding a $k \times k$ submatrix of maximum volume of a matrix $A$ is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of $A$. We show…

Let $A, B$ and $X$ be $n\times n$ matrices such that $A, B$ are positive semidefinite. We present some refinements of the matrix Cauchy-Schwarz inequality by using some integration techniques and various refinements of the Hermite--Hadamard…

Parity-time (PT) symmetric quantum theory can broaden the scope of quantum dynamics beyond unitary evolution which may lead to numerous counter-intuitive phenomena, including single-shot discrimination of non-orthogonal states, faster…

An equivalence of matrices via semi-tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices leads to the…

While the partial transpose operation appears in many fundamental results in quantum theory -- such as the Peres-Horodecki criterion for entanglement detection -- a physical interpretation of the partial transpose is lacking. In this work,…

In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities $A \otimes X \preceq B$. The purpose…

We have reexamined the moments of positive maps and the criterion based on these moments to detect entanglement. For two qubits, we observed that reduction map is equivalent to partial transpose map as the resulting matrices have the same…

Let $\mathbb{F}$ be an infinite field with characteristic different from two. For a graph $G=(V,E)$ with $V={1,...,n}$, let $S(G;\mathbb{F})$ be the set of all symmetric $n\times n$ matrices $A=[a_{i,j}]$ over $\mathbb{F}$ with…