Mutually unbiased maximally entangled bases from difference matrices

Unextendible maximally entangled bases and mutually unbiased bases

Isolated Hadamard Matrices from Mutually Unbiased Product Bases

A new construction of complex Hadamard matrices of composite order d = pq, with primes p, q, is presented which is based on pairs of mutually unbiased bases containing only product states. We illustrate the method for many product dimensions d < 100 by analytically deriving complex Hadamard matrices, both with zero and non-zero defect. In particular, we obtain at least 12 new isolated Butson-ty...

Real Mutually Unbiased Bases

We tabulate bounds on the optimal number of mutually unbiased bases in R. 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 number is at most either 2 or 3. We discuss the limitations of these methods when applied to all dimensions, shedding some light on the difficulty of obtaining tig...

Mutually unbiased bases and Hadamard matrices of order six

We report on a search for mutually unbiased bases MUBs in six dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a ...

Mutually Unbiased Bases, Generalized Spin Matrices and Separability

A collection of orthonormal bases for a d × d Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: |〈v, w〉|2 = 1 d . The MUB problem is to prove or disprove the the existence of a maximal set of d+1 bases. It has been shown in [W. K. Wootters, B. D. Fields, Annals of Physics, 191 no. 2, 363-381, (1989)] t...