Construction Of Complete Sets Research Articles

Constructions of complete sets

Abstract Constructing constant width sets or, more generally, complete sets in Banach spaces seems to be a not so easy task. A new construction working in separable Banach spaces is presented, and Bavaud’s and Lachand-Robert and Oudet’s constructions of complete sets are extended to a more general context.

Unitarily inequivalent mutually unbiased bases fornqubits

The standard construction of complete sets of mutually unbiased bases (MUBs) in prime power dimensions is based on the quadratic Gauss sums. We introduce complete MUB sets for three, four, and five qubits that are unitarily inequivalent to all existing MUB sets. These sets are constructed by using certain exponential sums, where the degree of the polynomial appearing in the exponent can be higher than 2. Every basis of these MUBs (except the computational) consists of two disjoint blocks of vectors with different factorization structures and associated with a unique hypergraph (or graph) that represents an interaction between the qubits.