Related papers: On orthostochastic, unistochastic and qustochastic…
We consider a random bistochastic matrix of size $n$ of the form $M Q$ where $M$ is a uniformly distributed permutation matrix and $Q$ is a given bistochastic matrix. Under mild sparsity and regularity assumptions on $Q$, we prove that the…
A new integrable model which is a variant of the one-dimensional Hubbard model is proposed. The integrability of the model is verified by presenting the associated quantum R-matrix which satisfies the Yang-Baxter equation. We argue that the…
We tabulate bounds on the optimal number of mutually unbiased bases in R^d. For most dimensions d, it can be shown with relatively simple methods that either there are no real orthonormal bases that are mutually unbiased or the optimal…
We introduce a class of regular unit Hadamard matrices whose entries consist of two complex numbers and their conjugates for a total of four complex numbers. We then show that these matrices are contained in the Bose-Mesner algebra of an…
We look at Bohemian matrices, specifically those with entries from $\{-1, 0, {+1}\}$. More, we specialize the matrices to be upper Hessenberg, with subdiagonal entries $\pm1$. Many properties remain after these specializations, some of…
In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for…
The Birkhoff polytope $\mathcal{B}_d$ consisting of all bistochastic matrices of order $d$ assists researchers from many areas, including combinatorics, statistical physics and quantum information. Its subset $\mathcal{U}_d$ of…
We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the…
A new construction of complex Hadamard matrices of composite order d=pq, with primes p,q, is presented which is based on pairs of mutually unbiased bases containing only product states. For product dimensions d < 100, we illustrate the…
Gerstenhaber's theorem states that the dimension of the unital algebra generated by two commuting $n\times n$ matrices is at most $n$. We study the analog of this question for positive matrices with a positive commutator. We show that the…
Unextendible sets of Mutually Unbiased Bases (MUBs) are examined from the point of view of complementary subalgebras. We show, that the linear span of less than $d+1$ factors of $M_d \otimes M_d$ does not contain pure states, and therefore…
Using reversible Hadamard difference sets, we construct symmetric Bush-type Hadamard matrices of order $4m^4$ for all odd integer $m$.
Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…
In our previous work, we introduced the following relaxation of the Hadamard property: a square matrix $H\in M_N(\mathbb R)$ is called "almost Hadamard" if $U=H/\sqrt{N}$ is orthogonal, and locally maximizes the 1-norm on O(N). We review…
A Butson Hadamard matrix $H$ has entries in the kth roots of unity, and satisfies the matrix equation $HH^{\ast} = nI_{n}$. We write $\mathrm{BH}(n, k)$ for the set of such matrices. A complete morphism of Butson matrices is a map…
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…
Two orthonormal bases B and B' of a d-dimensional complex inner-product space are called mutually unbiased if and only if |<b|b'>|^2=1/d holds for all b in B and b' in B'. The size of any set containing (pairwise) mutually unbiased bases of…
A collection of pairwise mutually unbiased bases (in short: MUB) in d>1 dimensions may consist of at most d+1 bases. Such "complete" collections are known to exists in C^d when d is a power of a prime. However, in general little is known…
Coquasitriangular universal ${\cal R}$ matrices on quantum Lorentz and quantum Poincar\'e groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on those objects…
Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in C^d\otimes…