Closing a single-copy gap to the Holevo bound with two-copy measurements

Abstract: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.

arXiv:2609.36874 [quant-ph]

(or arXiv:2609.36874v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.36874 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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