Quasiorthogonality of Commutative Algebras, Complex Hadamard Matrices, and Mutually Unbiased Measurements
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910919395639296 |
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| author | Kim, Sooyeong Kribs, David Lozano, Edison Pereira, Rajesh Plosker, Sarah |
| author_facet | Kim, Sooyeong Kribs, David Lozano, Edison Pereira, Rajesh Plosker, Sarah |
| contents | We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras of matrices, based on a matrix-theoretic notion we introduce that has a connection to complex Hadamard matrices. We also show how this new tool can yield significant information on the general non-commutative case. We finish by considering quasiorthogonality for the important subclass of commutative algebras that arise from mutually unbiased bases (MUBs) and mutually unbiased measurements (MUMs) in quantum information theory. We present a number of examples throughout the work, including a subclass that arises from group algebras and Latin squares. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasiorthogonality of Commutative Algebras, Complex Hadamard Matrices, and Mutually Unbiased Measurements Kim, Sooyeong Kribs, David Lozano, Edison Pereira, Rajesh Plosker, Sarah Quantum Algebra 47L90, 81P45, 05B20, 81P94 We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras of matrices, based on a matrix-theoretic notion we introduce that has a connection to complex Hadamard matrices. We also show how this new tool can yield significant information on the general non-commutative case. We finish by considering quasiorthogonality for the important subclass of commutative algebras that arise from mutually unbiased bases (MUBs) and mutually unbiased measurements (MUMs) in quantum information theory. We present a number of examples throughout the work, including a subclass that arises from group algebras and Latin squares. |
| title | Quasiorthogonality of Commutative Algebras, Complex Hadamard Matrices, and Mutually Unbiased Measurements |
| topic | Quantum Algebra 47L90, 81P45, 05B20, 81P94 |
| url | https://arxiv.org/abs/2504.18741 |