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quantum multi-parameter estimation Near Criticality in Ising-XXZ Diamond Structure

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2024年第10期63卷 1-14页

作者： Yan, Bing Chen, Ping North Univ China Shool Informat & Commun Engn Coll Rd 3 Taiyuan 030051 Shanxi Peoples R China North Univ China Shanxi Key Lab Signal Capturing & Proc Coll Rd 3 Taiyuan 030051 Shanxi Peoples R China

quantum Fisher information (QFI) is frequently utilized to investigate quantum criticality in various spin-chain models. However, little attention has been given to the quantum Fisher information matrix (QFIM) in this context. This study examines criticality and the strategy for the simultaneous estimation of multiple parameters using the QFIM in an Ising-XXZ diamond structure at finite temperatures. Our findings demonstrate that by analyzing the finite-temperature scaling behavior, the variances derived from the QFIM can accurately estimate the critical point in this model. Additionally, we observe that the behavior of variances is contingent upon both the system structure and the parameters used. Moreover, whether the multi-parameter simultaneous estimation strategy is advantageous over individual parameter estimation depends on the system structure, temperature, and the parameters applied.

关键词： quantum criticality quantum multi-parameter estimation quantum Fisher information matrix Ising-XXZ chain

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Feedback control and quantum error correction assisted quantum multi-parameter estimation

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Chinese Physics B 2023年第4期32卷 260-267页

作者：洪海源鲁秀娟匡森 Department of Automation University of Science and Technology of ChinaHefei 230027China Department of Mechanical Engineering The University of Hong KongHong Kong 999077China

quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum ***,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and *** this paper,a combined control scheme with feedback and quantum error correction(QEC)is proposed to achieve the Heisenberg limit in the presence of spontaneous emission,where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three *** an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be *** addition,the control scheme in this paper has a low-dimensional code *** the three components of a magnetic field,it can achieve the highest estimation precision with only a 2-dimensional code space,while at least a4-dimensional code space is required in the common optimal error correction protocols.

关键词： quantum multi-parameter estimation feedback control quantum error correction Heisenberg limit

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multi-parameter estimation beyond quantum Fisher information

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2020年第36期53卷 1-59页

作者： Demkowicz-Dobrzanski, Rafal Gorecki, Wojciech Guta, Madalin Univ Warsaw Fac Phys Pasteura 5 PL-02093 Warsaw Poland Univ Nottingham Sch Math Sci Univ Pk Nottingham NG7 2RD England

This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the quantum Fisher information concept. We discuss in detail the Holevo Cramer-Rao bound, the quantum local asymptotic normality approach as well as Bayesian methods. Even though the fundamental concepts in the field have been laid out more than forty years ago, a number of important results have appeared much more recently. Moreover, the field drew increased attention recently thanks to advances in practical quantum metrology proposals and implementations that often involve estimation of multiple parameters simultaneously. Since the topics covered in these review are spread in the literature and often served in a very formal mathematical language, one of the main goals of this review is to provide a largely self-contained work that allows the reader to follow most of the derivations and get an intuitive understanding of the interrelations between different concepts using a set of simple yet representative examples involving qubit and Gaussian shift models.

关键词： quantum metrology quantum Fisher information quantum local asymptotic normality Holevo Cramer-Rao bound quantum multi-parameter estimation

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Holevo bound independent of weight matrices for estimating two parameters of a qubit

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Chinese Physics B 2024年第2期33卷 137-143页

作者：牛畅郁司夏 Department of Modern Physics&Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences University of Science and Technology of ChinaHefei 230026China Hefei National Laboratory University of Science and Technology of ChinaHefei 230088China

Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically *** for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight *** we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial ***,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic *** weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation *** result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao *** generalizations are discussed.

关键词： quantum metrology quantum Fisher information Holevo bound quantum multi-parameter estimation

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