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.

翻译：我们提出一种基于代数的量子态层析算法，该算法利用特定可观测量的测量值来估计底层密度矩阵的结构化元素。在低秩假设下，其余元素可仅通过标准数值线性代数运算获得。所提出的代数矩阵补全框架适用于一大类通用的低秩混合量子态，与现有最先进方法相比，该算法在提供确定性恢复保证的同时，具有计算高效性。