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[2602.15202] Tomography by Design: An Algebraic Approach to Low-Rank Quantum States
Summary
This article presents an algebraic algorithm for quantum state tomography, focusing on low-rank quantum states and offering a computationally efficient method for estimating density matrices.
Why It Matters
The development of efficient algorithms for quantum state tomography is crucial in quantum computing and quantum information science. This research provides a new framework that enhances the accuracy and efficiency of estimating quantum states, which is vital for practical applications in quantum technologies.
Key Takeaways
- Introduces an algebraic approach to quantum state tomography.
- Focuses on low-rank quantum states for efficient density matrix estimation.
- Offers deterministic recovery guarantees compared to existing methods.
- Utilizes standard numerical linear algebra operations for computation.
- Broad applicability to various low-rank mixed quantum states.
Quantum Physics arXiv:2602.15202 (quant-ph) [Submitted on 16 Feb 2026] Title:Tomography by Design: An Algebraic Approach to Low-Rank Quantum States Authors:Shakir Showkat Sofi, Charlotte Vermeylen, Lieven De Lathauwer View a PDF of the paper titled Tomography by Design: An Algebraic Approach to Low-Rank Quantum States, by Shakir Showkat Sofi and 1 other authors View PDF HTML (experimental) Abstract: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. Comments: Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Signal Processing (eess.SP); Numerical Analysis (math.NA); Computation (stat.CO) MSC classes: 15A18, 15A69, 15A83, 62H25, 65F30, 65F55, 68Q01, 81P45, Cite as: arXiv:2602.15202 [quant-ph] (or arXiv:2602.15202v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.15202 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shakir Showkat Sofi [view email] [v1] Mon, 16 Feb 2026 21:31:47 UTC (102 KB) Full-te...
