近日，中山大学的庞盛世及其研究团队取得一项新进展。经过不懈努力，他们在量子计量中利用探针辅助相互作用实现海森堡定标。相关研究成果已于2024年12月3日在国际知名学术期刊《物理评论A》上发表。

在本文中，研究人员证明了如果测量方案设计得当，探针与辅助系统的额外维度之间的相互作用也可以提高参数估计的精度，使其超越标准量子极限并达到海森堡极限，而无需纠缠。量子费舍尔信息在演化时间上呈现出周期性模式，这意味着存在能够使量子费舍尔信息最大化的最优测量时间点。

通过对哈密顿量、探针和辅助系统的初始状态、相互作用强度以及测量时间点的优化，该研究方案在探针哈密顿量的参数方面，无论是演化时间还是探针数量，都达到了海森堡极限。

该研究方案具有两个特点：（i）可以通过探针的直积态达到海森堡极限；（ii）仅需对辅助系统进行局部测量即可，这两点都降低了实现海森堡极限所需的量子资源和实施复杂度。最后，本文还研究了噪声对该方案的影响。

据悉，海森堡极限是量子力学原理所允许的参数估计的最终精度极限，在经典领域中没有对应的极限，一直是量子计量学长期追求的目标。已知探针之间的相互作用可以在无需纠缠的情况下帮助达到海森堡极限。

附：英文原文

Title: Achieving Heisenberg scaling by probe-ancilla interaction in quantum metrology

Author: Jingyi Fan, Shengshi Pang

Issue&Volume: 2024/12/03

Abstract: The Heisenberg scaling is an ultimate precision limit of parameter estimation allowed by the principles of quantum mechanics, with no counterpart in the classical realm, and has been a long-pursued goal in quantum metrology. It has been known that interactions between the probes can help reach the Heisenberg scaling without entanglement. In this paper, we show that interactions between the probes and the additional dimensions of an ancillary system may also increase the precision of parameter estimation to surpass the standard quantum limit and attain the Heisenberg scaling without entanglement, if the measurement scheme is properly designed. The quantum Fisher information exhibits periodic patterns over the evolution time, implying the existence of optimal time points for measurements that can maximize the quantum Fisher information. By implementing optimizations over the Hamiltonian, the initial states of the probes and the ancillary system, the interaction strength, and the time points for measurements, our protocol achieves the Heisenberg scaling for the parameter of the probe Hamiltonian, in terms of both evolution time and probe number. Our protocol features two aspects: (i) the Heisenberg scaling can be achieved by a product state of the probes and (ii) mere local measurement on the ancilla is sufficient, both of which reduce the quantum resources and the implementation complexity to achieve the Heisenberg scaling. The paper is concluded by the investigation of the effects of noise on this protocol.

DOI: 10.1103/PhysRevA.110.062406

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.062406