Related papers: All Mutually Unbiased Bases in Dimensions Two to F…
We prove the following two results relating real mutually unbiased bases and representations of finite groups of odd order. Let $q$ be a power of 2 and $r$ a positive integer. Then we can find a $q^{2r}\times q^{2r}$ real orthogonal matrix…
The structural characterization of high-dimensional mutually unbiased bases (MUBs) by classifying MUBs subsets remains a major open problem. The existing methods not only fail to conclude on the exact classification, but also are severely…
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…
It was shown by LeCompte, Martin, and Oweans in 2010 that the existence of mutually unbiased Hadamard matrices and the identity matrix, which coincide with mutually unbiased bases, is equivalent to that of a $Q$-polynomial association…
In this paper, we consider the problem of Mutually Unbiased Bases in prime dimension $d$. It is known to provide exactly $d+1$ mutually unbiased bases. We revisit this problem using a class of circulant $d \times d$ matrices. The…
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…
Mutually unbiased bases (MUB) are useful in a number of research areas. The symmetry of MUB is an elusive and interesting subject. A (complete set of) MUB in dimension $d$ is sharply covariant if it can be generated by a group of order…
Mutually unbiased bases (MUBs) are highly symmetric bases on complex Hilbert spaces, and the corresponding rank-1 projective measurements are ubiquitous in quantum information theory. In this work, we study a recently introduced…
This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done…
A set of mutually unbiased bases (MUBs) is said to be unextendible if there does not exist another basis that is unbiased with respect to the given set. Here, we prove the existence of smaller sets of MUBs in prime-squared dimensions…
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…
We consider the problem of mutually unbiased bases as a polynomial optimization problem over the reals. We heavily reduce it using known symmetries before exploring it using two methods, combining a number of optimization techniques. The…
Constructing four six-dimensional mutually unbiased bases (MUBs) is an open problem in quantum physics and measurement. We investigate the existence of four MUBs including the identity, and a complex Hadamard matrix (CHM) of Schmidt rank…
It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those…
This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an…
Mutually Unbiased bases has various application in quantum information procession and coding theory. There can be maximum d + 1 MUBs in C^d and d/2 +1 MUBs in R^d. But , over R^d MUBs are known to be non existent when d is odd and for most…
In dimension $d$, Mutually Unbiased Bases (MUBs) are a collection of orthonormal bases over $\mathbb{C}^d$ such that for any two vectors $v_1, v_2$ belonging to different bases, the scalar product $|\braket{v_1|v_2}| = \frac{1}{\sqrt{d}}$.…
In this paper, we prove that the existence of a complete set of mutually unbiased bases (MUBs) in N-dimensional Hilbert space implies the existence of a complete set of mutually orthogonal Latin squares (MOLSs) of order N. In particular, we…
We consider the notion of unitary transformations forming bases for subspaces of $M(d,\mathbb{C})$ such that the square of Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case,…
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…