Related papers: Mutually unbiased bases via complex projective tri…
In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct…
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.…
An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional…
Suppose that for some unit vectors $b_1,\ldots b_n$ in $\mathbb C^d$ we have that for any $j\neq k$ $b_j$ is either orthogonal to $b_k$ or $|\langle b_j,b_k\rangle|^2 = 1/d$ (i.e. $b_j$ and $b_k$ are unbiased). We prove that if $n=d(d+1)$,…
In this paper we give explicit descriptions of complete sets of mutually unbiased bases (MUBs) and orthogonal decompositions of special Lie algebras $sl_n(\mathbb{C})$ obtained from commutative and symplectic semifields, and from some other…
There has been great interest in finding sets of $m$ mutually unbiased bases which are compatible with a given space $\mathbb{C}^d$, specially in physics due to their interesting applications in quantum information theory. Several general…
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…
Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We…
A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis with an arbitrary element of the other basis coincide. In case the dimension, $d$, of the considered Hilbert space is a power of…
Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of…
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…
We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363 (1989)] of a full set of mutually unbiased bases in a complex vector space of dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character vectors of the…
In this paper, we explore the concept of Mutually Unbiased Bases (MUBs) in discrete quantum systems. It is known that for dimensions $d$ that are powers of prime numbers, there exists a set of up to $d+1$ bases that form an MUB set.…
The study of Mutually Unbiased Bases continues to be developed vigorously, and presents several challenges in the Quantum Information Theory. Two orthonormal bases in $\mathbb C^d, B {and} B'$ are said mutually unbiased if $\forall b\in B,…
We study entanglement witness and present a construction of entanglement witnesses in terms of the mutually unbiased measurements (MUMs). These witnesses include the entanglement witnesses constructed from mutually unbiased bases (MUBs) as…
Large sets of equiangular lines are constructed from sets of mutually unbiased bases, over both the complex and the real numbers.
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…
Mutually Unbiased Bases (MUBs) constitute a fundamental geometric structure in quantum theory, known for providing an optimal measurement scheme for quantum state tomography. In prime and prime-power dimensions, analytical constructions of…
We derive a framework for quantifying entanglement in multipartite and high dimensional systems using only correlations in two unbiased bases. We furthermore develop such bounds in cases where the second basis is not characterized beyond…
We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most $d+1$ MUBs in ${\mathbb C}^d$. It may…