基于少量子比特测量的近最优量子计量学
Near-optimal quantum metrology with few-qubit measurements
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中文总结 AI 辅助
本研究提出仅用少量子比特测量的量子计量协议，其样本复杂度开销与量子比特数线性相关，对哈尔随机态可降至常数，建立了认证与计量的通用关联，逼近量子克拉美罗界并以哈密顿量估计实例验证。
中文摘要 AI 辅助
量子计量学用于解决量子系统中的参数估计问题，在科学和技术领域有广泛应用。针对多参数区域中多量子比特态的传统计量协议通常需要高度复杂的量子测量，导致量子资源成本大幅增加。本研究提出了一类仅使用少量子比特测量的计量协议，从而显著降低所需资源。对于任意纯态，其中一种协议的样本复杂度开销与量子比特数呈线性缩放，且无论待估计参数数量多少，其性能均逼近量子克拉美罗界。对于典型的哈尔随机态，该开销可降至常数。本研究的成果基于少量子比特测量量子态认证协议的最新进展，建立了认证与计量间的通用关联，即认证协议的精度决定计量开销。我们还通过基态哈密顿量估计的实例说明了所提方法。
英文摘要
Quantum metrology, which addresses parameter estimation in quantum systems, has broad applications across science and technology. Conventional metrology protocols for multi-qubit states in the multi-parameter regime typically require highly complex quantum measurements, leading to substantial quantum-resource costs. In this work, we introduce a family of metrology protocols that use only few-qubit measurements, thereby significantly reducing the required resources. For arbitrary pure states, one of our protocols approaches the quantum Cramér-Rao bound up to an overhead in sample complexity that scales linearly with the number of qubits, irrespective of the number of parameters to be estimated. For typical Haar-random states, this overhead can be reduced to a constant. Our results build on recent advances in quantum state certification protocols with few-qubit measurements: we establish a universal connection between certification and metrology in which the precision of the certification protocol determines the metrological overhead. We also illustrate our approach through an example of Hamiltonian estimation from ground states.
