Related papers: Schur multipliers and mixed unitary maps

Recently Rai obtained an upper bound for the order of the Schur multiplier of a $d$-generator special $p$-group when its derived subgroup has the maximum value $ p^{\frac{1}{2}d(d-1)}$ for $ d\geq 3 $ and $ p\neq 2. $ Here we try to obtain…

We devise an explicit method for computing combinatorial formulae for Hadamard products of certain rational generating functions. The latter arise naturally when studying so-called ask zeta functions of direct sums of modules of matrices or…

From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al. asked to obtain the Schur multiplier and the representation of a group $G$, when $G$ is a special $p$-group minimally generated by $d$ elements and…

We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable…

Striking result of Vyb\'{\i}ral [\textit{Adv. Math.} 2020] says that Schur product of positive matrices is bounded below by the size of the matrix and the row sums of Schur product. Vyb\'{\i}ral used this result to prove the Novak's…

We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…

We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when…

In the theory of quantum information, the mixed-unitary quantum channels, for any positive integer dimension $n$, are those linear maps that can be expressed as a convex combination of conjugations by $n\times n$ complex unitary matrices.…

In this paper, using a relationship between the Schur multiplier of a group $G$, the fundamental group, and the second homology group of the Eilenberg-MacLane space of $G$, we present new proofs for some famous properties of the Schur…

Correlators in monomial Hermitian matrix model strongly depend on the choice of eigenvalue integration contours. We express Schur correlator in case of several different integration contours (mixed phase case) as a sum over products of…

Matrix-product unitaries (MPU) are 1D tensor networks describing time evolution and unitary symmetries of quantum systems, while their action on states by construction preserves the entanglement area law. MPU which are formed by a single…

We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which…

Using techniques from integrable systems, we obtain a number of exact results for random partitions. In particular, we prove a simple formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching…

This paper is a sequel of arXiv:2109.06394. In this paper, we consider a kind of inverse problem of multipliers. The problem is to count number of isospectral correspondences, correspondences which has the same combination of multipliers.…

For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.

We study mixed unitary channels generated by finite subgroups of the group of all unitary operators in a Hilbert space. Based on the majorization theory we introduce techniques allowing to calculate different characteristics of output…

Schur decompositions and the corresponding Schur forms of a single matrix, a pair of matrices, or a collection of matrices associated with the periodic eigenvalue problem are frequently used and studied. These forms are upper-triangular…

We give an explicit combinatorial formula for the Schur expansion of Macdonald polynomials indexed by partitions with second part at most two. This gives a uniform formula for both hook and two column partitions. The proof comes as a…

We prove new interaction Morawetz type (correlation) estimates in one and two dimensions. In dimension two the estimate corresponds to the nonlinear diagonal analogue of Bourgain's bilinear refinement of Strichartz. For the 2d case we…

The partition function for unitary two matrix models is known to be a double KP tau-function, as well as providing solutions to the two dimensional Toda hierarchy. It is shown how it may also be viewed as a Borel sum regularization of…