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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.15202 |
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| _version_ | 1866917277725622272 |
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| author | Sofi, Shakir Showkat Vermeylen, Charlotte De Lathauwer, Lieven |
| author_facet | Sofi, Shakir Showkat Vermeylen, Charlotte De Lathauwer, Lieven |
| contents | We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be obtained solely using standard numerical linear algebra operations. The proposed algebraic matrix completion framework applies to a broad class of generic, low-rank mixed quantum states and, compared with state-of-the-art methods, is computationally efficient while providing deterministic recovery guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tomography by Design: An Algebraic Approach to Low-Rank Quantum States Sofi, Shakir Showkat Vermeylen, Charlotte De Lathauwer, Lieven Quantum Physics Artificial Intelligence Numerical Analysis Signal Processing Computation 15A18, 15A69, 15A83, 62H25, 65F30, 65F55, 68Q01, 81P45, We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be obtained solely using standard numerical linear algebra operations. The proposed algebraic matrix completion framework applies to a broad class of generic, low-rank mixed quantum states and, compared with state-of-the-art methods, is computationally efficient while providing deterministic recovery guarantees. |
| title | Tomography by Design: An Algebraic Approach to Low-Rank Quantum States |
| topic | Quantum Physics Artificial Intelligence Numerical Analysis Signal Processing Computation 15A18, 15A69, 15A83, 62H25, 65F30, 65F55, 68Q01, 81P45, |
| url | https://arxiv.org/abs/2602.15202 |