Isolated Hadamard Matrices from Mutually Unbiased Product Bases

Daniel McNulty; Stefan Weigert

doi:10.1063/1.4764884

Isolated Hadamard Matrices from Mutually Unbiased Product Bases

Daniel McNulty, Stefan Weigert

Mathematics

Research output: Contribution to journal › Article › peer-review

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. 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-type Hadamard matrices of orders ranging from 9 to 91.

Original language	English
Article number	122202
Number of pages	16
Journal	Journal of Mathematical Physics
Volume	53
Issue number	2
Early online date	28 Nov 2012
DOIs	https://doi.org/10.1063/1.4764884
Publication status	Published - Nov 2012

Keywords

Quantum Physics (quant-ph)

Access to Document

10.1063/1.4764884

http://jmp.aip.org/resource/1/jmapaq/v53/i12/p122202_s1

Cite this

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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. 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-type Hadamard matrices of orders ranging from 9 to 91. ",

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AB - 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-type Hadamard matrices of orders ranging from 9 to 91.

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