Two-Unitary Complex Hadamard Matrices of Order $36$

Abstract

A family of two-unitary complex Hadamard matrices (CHM) stemming from a particular matrix, of size $36$ is constructed. Every matrix in this orbit remains unitary after operations of partial transpose and reshuffling which makes it a distinguished subset of CHM. It provides a novel solution to the quantum version of the Euler problem, in which each field of the Graeco-Latin square of size six contains a symmetric superposition of all $36$ officers with phases being multiples of sixth root of unity. This simplifies previously known solutions as all amplitudes of the superposition are equal and the set of phases consists of $6$ elements only. Multidimensional parameterization allows for more flexibility in a potential experimental realization.

13 pages, 1 figure

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Cited by in corpus (4)

• Operator dynamics and entanglement in space-time dual Hadamard lattices
• Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States
• Absolutely maximally entangled pure states of multipartite quantum systems
• Equivalence of Complex Hadamard Matrices