相关论文: Mutually Unbiased Bases and The Complementarity Po…
Every convex polygon with $n$ vertices is a linear projection of a higher-dimensional polytope with at most $147\,n^{2/3}$ facets.
We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions. An algebraic description of a SIC-POVM in dimension six is…
We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters…
Finding four six-dimensional mutually unbiased bases (MUBs) containing the identity matrix is a long-standing open problem in quantum information. We show that if they exist, then the $H_2$-reducible matrix in the four MUBs has exactly nine…
We express Alltop's construction of mutually unbiased bases as orbits under the Weyl-Heisenberg group in prime dimensions and find a related construction in dimensions 2 and 4. We reproduce Alltop's mutually unbiased bases using abelian…
We show that k=w+2 mutually unbiased bases can be constructed in any square dimension d=s^2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k,s)-nets (which can…
The construction of optimal line packings in real or complex Euclidean spaces has shown to be a tantalizingly difficult task, because it includes the problem of finding maximal sets of equiangular lines. In the regime where equiangular…
In this paper we define and investigate a class of polytopes which we call "vertex generated" consisting of polytopes which are the average of their $0$ and $n$ dimensional faces. We show many results regarding this class, among them: that…
Unextendible product bases (UPBs) provide a versatile tool with various applications across different areas of quantum information theory. Their comprehensive characterization is thus of great importance and has been a subject of vital…
A set of $b$ mutually unbiased bases (MUBs) in $\mathbb{C}^d$ (for $d > 1$) comprises $bd$ vectors in $\mathbb{C}^d$, partitioned into $b$ orthogonal bases for $\mathbb{C}^d$ such that the pairwise angle between all vectors from distinct…
The paper gives a short introduction to mutually unbiased bases and the Welch bounds and demonstrates that the latter is a good technical tool to explore the former. In particular, a criterion for a system of vectors to satisfy the Welch…
A biconvex polytope is a classical and tropical convex hull of finitely many points. Given a biconvex polytope, for each vertex of it we construct a directed bigraph and a gammoid so that the collection of base polytopes of those gammoids…
In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base…
We study the relationship between Bell states, finite groups and complete sets of bases. We show how to obtain a set of N+1 bases in which Bell states are invariant. They generalize the X, Y and Z qubit bases and are associated to groups of…
A Galois unitary is a generalization of the notion of anti-unitary operators. They act only on those vectors in Hilbert space whose entries belong to some chosen number field. For Mutually Unbiased Bases the relevant number field is a…
Two interesting phenomena for the construction of quantum states are that of mutually unbiased bases and that of balanced states. We explore a constructive approach to each phenomenon that involves orthogonal polynomials on the unit circle.…
We consider the primitive quaternionic reflection groups of type P for H^2 that are obtained from Blichfeldt's collineation groups for C^4.These are seen to be intimately related to the maximal set of five quaternionic mutually unbiased…
In quantum mechanics some properties are maximally incompatible, such as the position and momentum of a particle or the vertical and horizontal projections of a 2-level spin. Given any definite state of one property the other property is…
We introduce the notion of the unextendible maximally entangled basis (UMEB), a set of orthonormal maximally entangled states in d \times d consisting of fewer that d^2 vectors which have no additional maximally entangled vectors orthogonal…
We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the squares of the moduli of their scalar products are equal to zero, one, or 1/d. These sets will be called a MU constellation, and…