Related papers: Constructing mutually unbiased bases from unextend…
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…
A set of vectors of equal norm in $\mathbb{C}^d$ represents equiangular lines if the magnitudes of the Hermitian inner product of every pair of distinct vectors in the set are equal. The maximum size of such a set is $d^2$, and it is…
Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of…
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…
The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six…
I introduce a new notion, that extends the mutually unbiased bases (MUB) conditons to more than two bases. These, I call the nUB conditions, and the corresponding bases $n$-fold unbiased. They naturally appear while optimizing generic…
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 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…
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…
Construction of a large class of Mutually Unbiased Bases (MUBs) for non-prime power composite dimensions ($d = k\times s$) is a long standing open problem, which leads to different construction methods for the class Approximate MUBs (AMUBs)…
For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases…
We examine the problem of exhibiting Bell nonlocality for a two-qudit entangled pure state using a randomly chosen set of mutually unbiased bases (MUBs). Interestingly, even if we employ only two-setting Bell inequalities, we find a…
The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in…
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…
The problem of finding provably maximal sets of mutually unbiased bases in $\mathbb{C}^d$, for composite dimensions $d$ which are not prime powers, remains completely open. In the first interesting case, $d=6$, Zauner predicted that there…
We study the problem of constructing mutually unbiased bases in dimension six. This approach is based on an efficient numerical method designed to find solutions to the quantum state reconstruction problem in finite dimensions. Our…
We establish a connection between the problem of constructing maximal collections of mutually unbiased bases (MUBs) and an open problem in the theory of Lie algebras. More precisely, we show that a collection of m MUBs in K^n gives rise to…
All mutually unbiased bases in dimension six consisting of product states only are constructed. Several continuous families of pairs and two triples of mutually unbiased product bases are found to exist but no quadruple. The exhaustive…
In quantum information, complementarity of quantum mechanical observables plays a key role. If a system resides in an eigenstate of an observable, the probability distribution for the values of a complementary observable is flat. The…
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…