一类具有广泛纠缠和魔力的混合态的样本高效层析
Sample-Efficient Tomography of a Class of Mixed States with Extensive Entanglement and Magic
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中文总结 AI 辅助
本文引入Clifford编码块乘积态，证明在固定块大小下，利用Clifford保持的Pauli相关性可多项式副本重建高度纠缠且魔力的混合态，提出潜在框架有界复杂性作为量子态可学习性的组织原则。
中文摘要 AI 辅助
通用多量子比特量子态的完整层析需要指数多的副本，而适当的结构约束可以使重建具有样本高效性。现有方法利用例如受限的纠缠结构、低魔力或受约束的态制备电路。这里我们考虑一类可以同时展现广泛纠缠和广泛魔力的混合态。具体地，我们引入Clifford编码块乘积（CEBP）态，通过将未知的全局Clifford酉算子应用于支持在未知有界大小块上的任意混合态的张量积而获得。我们证明，对于固定的块大小，CEBP态可以利用多项式多的副本通过利用Clifford保持的Pauli相关性来恢复潜在结构并将剩余问题简化为局部层析来重建。我们的结果表明，样本高效的层析可以源于潜在框架中的有界复杂性，即使物理态是高度纠缠、高度魔力且混合的，并建议模结构化变换的复杂性作为量子态可学习性的更广泛组织原则。
英文摘要
Full tomography of a generic many-qubit quantum state requires exponentially many copies, while suitable structural constraints can make reconstruction sample-efficient. Existing approaches exploit, for example, limited entanglement structure, low magic, or constrained state-preparation circuits. Here we consider a class of mixed states that can simultaneously exhibit extensive entanglement and extensive magic. Specifically, we introduce Clifford-encoded block-product (CEBP) states, obtained by applying an unknown global Clifford unitary to a tensor product of arbitrary mixed states supported on unknown blocks of bounded size. We show that, for a fixed block size, CEBP states can be reconstructed using polynomially many copies by exploiting Clifford-preserved Pauli correlations to recover the latent structure and reduce the remaining problem to local tomography. Our result demonstrates that sample-efficient tomography can arise from bounded complexity in a latent frame even when the physical state is highly entangled, highly magical, and mixed, and suggests complexity modulo structured transformations as a broader organizing principle for quantum-state learnability.
发表机构
- University of Southern California（南加州大学）
机构由 AI 辅助整理，请以论文原文为准。
