Tomography by Design: An Algebraic Approach to Low-Rank Quantum States
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.
Fields of Study & Subjects
Quantum Information and Cryptography
Quantum Computing Algorithms and Architecture
Sparse and Compressive Sensing Techniques
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 16 February 2026
- Language
- EN
- Document type
- Preprint