Related papers: Isolated Hadamard Matrices from Mutually Unbiased …
We study the mathematical structures and relations among some quantities in the theory of quantum entanglement, such as separability, weak Schmidt decompositions, Hadamard matrices etc.. We provide an operational method to identify the…
We consider generic degenerate subvarieties $X_i\subset\mathbb{P}^n$. We determine an integer $N$, depending on the varieties, and for $n\geq N$ we compute dimension and degree formulas for the Hadamard product of the varieties $X_i$.…
We study birational transformations of the projective space originating from lattice statistical mechanics, specifically from various chiral Potts models. Associating these models to \emph{stable patterns} and \emph{signed-patterns}, we…
A Butson-Hadamard matrix H is a square matrix of dimension n whose entries are complex roots of unity such that HH*= nI. In the first part of this work, some new results on generalized Gray map are studied. In the second part, codes…
We show that any two Hadamard subfactors arising from a pair of distinct complex Hadamard matrices of order 3 are either equal or conjugate by a unitary in the relative commutant of their intersection. Moreover, when the Hadamard subfactors…
We construct an extended Hubbard model with open boundaries from a $R$-matrix based on the $U_q[Osp(2|2)]$ superalgebra. We study the reflection equation and find two classes of diagonal solutions. The corresponding one-dimensional open…
We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets…
We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are…
Basic matrices are defined which provide unique building blocks for the class of normal matrices which include the classes of unitary and Hermitian matrices. Unique builders for quantum logic gates are hence derived since a quantum logic…
In this paper, we introduce a particular class of matrices. We study the concept of a matrix to be \emph{balanced}. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix…
In this paper we construct a new, previously unknown four-parameter family of complex Hadamard matrices of order 6, the entries of which are described by algebraic functions of roots of various sextic polynomials. We conjecture that the…
We generalize the concept of mutually unbiased bases (MUB) to measurements which are not necessarily described by rank one projectors. As such, these measurements can be a useful tool to study the long standing problem of the existence of…
Analogous to the notion of mutually unbiased bases for Hilbert spaces, we consider mutually unbiased unitary bases (MUUB) for the space of operators, $M(d, \mathbb{C})$, acting on such Hilbert spaces. The notion of MUUB reflects the…
We provide a construction of sets of (d/2+1) mutually unbiased bases (MUBs) in dimensions d=4,8 using maximal commuting classes of Pauli operators. We show that these incomplete sets cannot be extended further using the operators of the…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
For a family of unital free *-algebras with a family of states on them, we construct a sequence of noncommutative probability spaces, which are tensor product algebras with tensor product states and which approximate the free product of…
We give an entirely new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique in additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most…
A simple recipe for generating a complete set of mutually unbiased bases in dimension (2j+1)**e, with 2j + 1 prime and e positive integer, is developed from a single matrix acting on a space of constant angular momentum j and defined in…
In this paper we provide an analytical procedure which leads to a system of $(n-2)^2$ polynomial equations whose solutions give the parameterisation of the complex $n\times n$ Hadamard matrices. It is shown that in general the Hadamard…
Mutually unbiased bases (MUB) have many applications in quantum information processing and quantum cryptography. Several complex MUB's in $\mathbb{C}^d$ for some dimension $d$ and with larger size have been constructed. On the other hand,…