用双副本测量弥合到Holevo界的单副本差距
Closing a single-copy gap to the Holevo bound with two-copy measurements
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- Unitary Foundation（Unitary基金会）
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中文总结 AI 辅助
通过构造三参数秩二模型，证明Holevo界在双副本下可达到，并实验验证双副本集体测量优于单副本及分离测量，揭示精度可达性与模型结构及集体测量资源相关。
中文摘要 AI 辅助
Holevo Cramér-Rao界设定了量子多参数估计的渐近可达到精度，但其在有限量子态副本下的可达到性在一般情况下仍未解决。对于双参数估计模型，单副本最优值与Holevo界之间的差距在任何有限副本数下持续存在，而更高参数情形此前仍属开放问题。在此，我们通过构造一个三参数秩二模型，否证了超过两个参数时有限副本差距的普遍持续性，该模型的Holevo界在单副本下不可达到，但在双副本下精确达到。我们进一步证明了任意参数数量的满秩模型下有限副本差距的持续性。随后，我们使用超导量子比特对所构造模型实验实现了双副本集体测量。我们观察到，双副本估计误差低于由态层析确定的单副本及分离测量界。通过引入受控退极化，我们展示了这一精度优势在有限噪声范围内持续存在。我们的结果将终极量子精度的可达到性与多参数估计模型的结构以及集体测量可用的资源联系起来。
英文摘要
The Holevo Cramér-Rao bound sets the asymptotically attainable precision of quantum multiparameter estimation, but its attainability with finite quantum state copies remains unresolved in general. While a gap between the single-copy optimum and the Holevo bound persists at any finite copy number for two-parameter estimation models, the higher-parameter case has remained open. Here we disprove universal finite-copy gap persistence beyond two parameters by constructing a three-parameter rank-two model whose Holevo bound is unattainable with one copy but attained exactly with two. We further prove finite-copy persistence for full-rank models with any number of parameters. We then experimentally implement the two-copy collective measurement for the constructed model using superconducting qubits. We observe a two-copy estimation error below the single-copy and separate-measurement bounds determined from state tomography. By introducing controlled depolarization, we show that this precision advantage persists over a finite noise range. Our results connect the attainability of ultimate quantum precision to the structure of the multiparameter estimation model and the resources available for collective measurements.
