Two-Unitary Complex Hadamard Matrices of Order $36$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929351923073024 |
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| author | Bruzda, Wojciech Życzkowski, Karol |
| author_facet | Bruzda, Wojciech Życzkowski, Karol |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01671 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-Unitary Complex Hadamard Matrices of Order $36$ Bruzda, Wojciech Życzkowski, Karol Quantum Physics 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. |
| title | Two-Unitary Complex Hadamard Matrices of Order $36$ |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.01671 |