Tomography by Design: An Algebraic Approach to Low-Rank Quantum States

• URL: http://arxiv.org/abs/2602.15202v1
• Date: Mon, 16 Feb 2026 21:31:47 GMT
• Title: Tomography by Design: An Algebraic Approach to Low-Rank Quantum States
• Authors: Shakir Showkat Sofi, Charlotte Vermeylen, Lieven De Lathauwer,
• Abstract summary: We present an algorithm for quantum state tomography that estimates structured entries of the underlying density matrix.<n>The proposed framework applies to a broad class of generic, low-rank mixed quantum states.
• Score: 0.802904964931021
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

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