Eldredge Zachary, Foss-Feig Michael, Gross Jonathan A, Rolston S L, Gorshkov Alexey V
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Phys Rev A (Coll Park). 2018;97. doi: 10.1103/PhysRevA.97.042337.
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.
量子计量学研究表明，与非纠缠态相比，使用多体纠缠态可提高测量灵敏度。在本文中，我们在被测物理量是分别与每个量子比特耦合的参数的线性函数的情况下，量化了纠缠的计量优势。我们首先将海森堡极限推广到量子网络中非局域可观测量的测量，基于多参数量子费舍尔信息推导出一个界限。然后我们提出了可以利用格林伯格 - 霍恩 - 泽林格（GHZ）态或自旋压缩态的测量协议，并表明在GHZ态的情况下该协议是最优的，即它达到了我们推导的界限。我们还确定了纳米级磁共振成像作为这项技术的一个有前景的应用场景。
