用代数方法高效重建低秩量子态，无需随机采样
Tomography by Design: An Algebraic Approach to Low-Rank Quantum States
- 基于可观测量构建代数矩阵补全框架
- 在低秩假设下仅需标准线性代数运算即可恢复全部矩阵元素
- 计算高效且有确定性恢复保证，适合实验物理与量子信息研究者
我们提出一种代数算法用于量子态层析，通过测量特定可观测量来估计密度矩阵的结构化元素。在低秩假设下，剩余元素仅需标准数值线性代数操作即可获得。所提出的代数矩阵补全框架适用于广泛类别的通用低秩混合量子态，相较于现有最优方法，计算更高效且具有确定性恢复保证。
原文摘要 · Abstract (English)
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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