Isolated Hadamard Matrices from Mutually Unbiased Product Bases
Daniel McNulty, Stefan Weigert
TL;DR
This paper introduces a novel method for constructing complex Hadamard matrices of composite order using mutually unbiased product bases, leading to the discovery of numerous new matrices, including isolated ones of Butson type.
Contribution
The paper presents a new construction technique for complex Hadamard matrices based on mutually unbiased product bases, expanding the known set of such matrices.
Findings
Derived many previously unknown complex Hadamard matrices under 100
Obtained at least 12 new isolated matrices of Butson type
Matrices range from order 9 to 91
Abstract
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. For product dimensions d < 100, we illustrate the method by deriving many previously unknown complex Hadamard matrices. We obtain at least 12 new isolated matrices of Butson type, with orders ranging from 9 to 91.
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