SU2 Nonstandard Bases: Case of Mutually Unbiased Bases

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...

Constructions of Mutually Unbiased Bases

Two orthonormal bases B andB′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |〈b|b〉| = 1/d holds for all b ∈ B and b′ ∈ B′. The size of any set containing pairwise mutually unbiased bases of C cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of thi...

Unextendibility of Mutually Unbiased Bases

Besides being of independent interest in understanding the structure of (partial) MUB collections and their conjugacy classes, satisfactory answers to these questions will help the following investigations: – the search for lower bounds on the number of MUBs and specifically for efficient constructions; – the search for upper bounds on the number of MUBs even for small non-prime-power dimension...

Entanglement in mutually unbiased bases

One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon manifests itself most strongly when observables are related to mutually unbiased bases. In this paper, we shed some light on the connection between mutually unbiased bases and another essential feature of quantum mechanics, quantum entanglement. It is shown tha...

Unextendible maximally entangled bases and mutually unbiased bases