Left Image: In generalized phase estimation tasks, local interactions and long-range interactions have a substantial impact on the accuracy of phase estimation. For unentangled initial states, it is difficult to surpass the shot noise limit even by using local multi-body interaction Hamiltonians to encode parameters. This indicates that long-range interactions and entanglement of the initial state are important quantum resources for achieving Heisenberg-limited measurement precision. For more information, please refer to the related article in Physical Review Letters.
Right Image: By placing a three-dimensional yttrium iron garnet (YIG) crystal in an optical cavity, (a) the generated magnons can sense weak magnetic fields B. Through the dynamic coupling between magnons and photons, the information of the parameter B to be estimated can be transferred to photons. (b) Under achievable experimental conditions, high-precision estimation of the magnetic field can be achieved by measuring the evolution of the photonic state, which is known as partial estimation theory. (c) By utilizing single-mode photonic squeezed states, the measurement precision of weak magnetic fields B can be improved to the Heisenberg limit of photon numbers in the weak coupling region. Critically enhanced quantum precision measurement can be achieved in the strong coupling region. For more information, please refer to the Physical Review B Letter article.
Quantum entanglement plays a crucial role in the field of quantum information processing. A deep understanding of the role of quantum entanglement in quantum metrology is essential for designing high-precision quantum measurement techniques. In traditional quantum phase estimation tasks, studies have shown that the use of GHZ-type entangled states can effectively improve measurement precision compared to unentangled states, elevating the classical shot noise limit (SNL) to the Heisenberg limit (HL). This discovery not only allows researchers to recognize that entanglement is an important resource for achieving high-precision quantum measurements but also drives research on the theoretical description of quantum multi-body entanglement in metrology. However, researchers have also found that in some precision measurement tasks, the optimal quantum state may be an unentangled state. Therefore, understanding the source of quantum advantage in quantum precision measurement is an urgent theoretical question, especially for tasks beyond quantum phase estimation.
In the related research published in Physical Review Letters, the research team achieved generalized phase estimation tasks by introducing quantum multi-body interactions among independent sensors (see left image). First, the researchers derived a universal bound on the growth of Quantum Fisher Information (QFI) under arbitrary dynamics and initial states. QFI, as a core concept in quantum metrology, can be used to quantify the precision of parameter estimation. By applying this bound to generalized phase estimation tasks and utilizing the famous Lieb-Robinson bound to handle situations with local short-range interactions, it was proven that for unentangled initial states and non-degenerate ground states of local and gapped Hamiltonians, QFI cannot surpass the SNL. This proof clarifies the importance of initial state entanglement and long-range interactions in achieving quantum-enhanced sensing in generalized phase estimation tasks (see left image). Additionally, the study revealed extensive connections between many-body physics, quantum control theory, quantum chaos, operator growth, and quantum metrology. The related research was published on March 5th under the title Universal Shot-Noise Limit for Quantum Metrology with Local Hamiltonians. Dr. SHI Hailong, a postdoctoral fellow at the Italian National Institute of Optics and a former graduate student of researcher GUAN Xiwen at APM, is the first author of the article and completed the majority of the computational work during his doctoral studies. Researcher YANG Jing from the Nordic Institute for Theoretical Physics is the corresponding author, and Researcher GUAN Xiwen participated in the collaborative research.
In the related research work published in Physical Review B, the research team investigated the task of Gaussian state precision measurement in the context of partial measurement estimation theory, which requires accessing only a portion of the system in practical experiments (as shown in the right figure). The team established a precise relationship between the Quantum Fisher Information (QFI) and bipartite entanglement, clarifying the significant role of bipartite entanglement in dynamical encoding. However, the presence of bipartite entanglement during the measurement process significantly degrades the final measurement accuracy. The study suggests that these conclusions could be verified in experimentally feasible cavity magnetic systems. Additionally, the research team further demonstrated that within the weak coupling region, the measurement accuracy can reach the Heisenberg limit. In the strong coupling region, quantum criticality can effectively enhance measurement accuracy. This work reveals the role of entanglement in quantum precision measurement tasks and provides important insights for research on quantum-enhanced precision measurement at criticality. The work was published on January 16th as a Letter titled Quantum-Enhanced Metrology in Cavity Magnonics in Physical Review B. PhD student WAN Qingkun and graduated doctoral candidate SHI Hailong from APM are co-first authors, while SHI Hailong and GUAN Xiwen are co-corresponding authors.
The related research was supported by the National Natural Science Foundation of China, the European Union funds, and the Wallenberg Network and Quantum Information Research Program in Sweden.
Link to the article:
《Physical Review Letters》
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.100803
《Physical Review B》
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.L041301