Title: Designing Tomography: An Algebraic Strategy for Low-Rank Quantum States

Abstract: This work introduces an algebraic algorithm for quantum state tomography that utilizes measurements of specific observables to estimate the structured components of the target density matrix. When low-rank conditions are met, the remaining matrix elements can be derived exclusively through conventional numerical linear algebra techniques. Our proposed algebraic matrix completion scheme is applicable to a wide range of generic, low-rank mixed quantum states. It offers deterministic recovery guarantees and demonstrates superior computational efficiency relative to existing state-of-the-art methods.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC