Isolated Hadamard Matrices from Mutually Unbiased Product Bases

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.

21 pages, identical to published version

References in corpus (11)

• On mutually unbiased bases
• A new proof for the existence of mutually unbiased bases
• All Teleportation and Dense Coding Schemes
• Mubs and Hadamards of Order Six
• Entanglement in mutually unbiased bases
• Construction, classification and parametrization of complex Hadamard matrices
• The Limited Role of Mutually Unbiased Product Bases in Dimension Six
• MUBs inequivalence and affine planes
• Complex Hadamard matrices of order 6: a four-parameter family
• Hadamard Matrices from Mutually Unbiased Bases
• Families of complex Hadamard matrices

Cited by in corpus (5)

• $BCCB$ complex Hadamard matrices of order 9, and MUBs
• A new method to construct families of complex Hadamard matrices in even dimensions
• Block-Circulant Complex Hadamard Matrices
• Isolated partial Hadamard matrices, and related topics
• Equivalence of Complex Hadamard Matrices