Evaluating the quantum optimal biased bound in a unitary evolution process

Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task. Nevertheless, most actual estimators are usually biased in the limited number of trials. For this reason, we introduce two effective error bounds for biased estimators based on a unitary evolution process in the framework of the quantum optimal biased bound. Furthermore, we show their estimation performance by two specific examples of the unitary evolution process, including the phase encoding and the SU(2) interferometer process. Our findings will provide an useful guidance for finding the precision limit of unknown parameters.

[1]  W. Ye,et al.  Intramode-correlation–enhanced simultaneous multiparameter-estimation precision , 2022, Physical Review A.

[2]  Chun-Hua Yuan,et al.  Protection of Noise Squeezing in a Quantum Interferometer with Optimal Resource Allocation. , 2022, Physical review letters.

[3]  Haidong Yuan,et al.  QuanEstimation: An open-source toolkit for quantum parameter estimation , 2022, Physical Review Research.

[4]  R. Meyer,et al.  Parameter estimation with gravitational waves , 2022, Reviews of Modern Physics.

[5]  W. Ye,et al.  Evaluating the quantum Ziv-Zakai bound for phase estimation in noisy environments. , 2022, Optics express.

[6]  Anthony J. Brady,et al.  Entangled Sensor-Networks for Dark-Matter Searches , 2022, PRX Quantum.

[7]  G. Agarwal,et al.  Quantifying quantum-amplified metrology via Fisher information , 2022, Physical Review Research.

[8]  Haidong Yuan,et al.  Optimal Scheme for Quantum Metrology , 2021, Advanced Quantum Technologies.

[9]  J. Shapiro,et al.  Ultimate Accuracy Limit of Quantum Pulse-Compression Ranging. , 2021, Physical review letters.

[10]  M. Gessner,et al.  Improving sum uncertainty relations with the quantum Fisher information , 2021, Physical Review Research.

[11]  G'eza T'oth,et al.  Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices , 2021, Physical Review Research.

[12]  Liang Jiang,et al.  Distributed quantum phase sensing for arbitrary positive and negative weights , 2021, Physical Review Research.

[13]  R. Demkowicz-Dobrzański,et al.  Multiple-Phase Quantum Interferometry: Real and Apparent Gains of Measuring All the Phases Simultaneously. , 2021, Physical review letters.

[14]  K. C. Tan,et al.  Fisher Information Universally Identifies Quantum Resources. , 2021, Physical review letters.

[15]  Zeyang Liao,et al.  Improved phase sensitivity in a quantum optical interferometer based on multiphoton catalytic two-mode squeezed vacuum states , 2021 .

[16]  Nicolai Friis,et al.  Bayesian parameter estimation using Gaussian states and measurements , 2020, Quantum Science and Technology.

[17]  P. Lam,et al.  Efficient computation of the Nagaoka–Hayashi bound for multiparameter estimation with separable measurements , 2020, npj Quantum Information.

[18]  Rafal Demkowicz-Dobrzanski,et al.  Multi-parameter estimation beyond quantum Fisher information , 2020, Journal of Physics A: Mathematical and Theoretical.

[19]  Earl T. Campbell,et al.  Tight Bounds on the Simultaneous Estimation of Incompatible Parameters , 2019, Physical Review X.

[20]  L. Vorster,et al.  Bound , 2019, SIGGRAPH ASIA Computer Animation Festival.

[21]  M. S. Zubairy,et al.  Operational resource theory of nonclassicality via quantum metrology , 2019 .

[22]  Pieter Kok,et al.  Geometric perspective on quantum parameter estimation , 2019, AVS Quantum Science.

[23]  Francesco Albarelli,et al.  Evaluating the Holevo Cramér-Rao Bound for Multiparameter Quantum Metrology. , 2019, Physical review letters.

[24]  Jesús Rubio,et al.  Bayesian multiparameter quantum metrology with limited data , 2019, Physical Review A.

[25]  Wei Ye,et al.  Improvement of self-referenced continuous-variable quantum key distribution with quantum photon catalysis. , 2019, Optics express.

[26]  Jesús Rubio,et al.  Quantum metrology in the presence of limited data , 2018, New Journal of Physics.

[27]  K. C. Tan,et al.  Nonclassicality as a Quantifiable Resource for Quantum Metrology. , 2018, Physical review letters.

[28]  Jeffrey H. Shapiro,et al.  Distributed Quantum Sensing Using Continuous-Variable Multipartite Entanglement , 2017, 2018 Conference on Lasers and Electro-Optics (CLEO).

[29]  J. Dunningham,et al.  Multiparameter Estimation in Networked Quantum Sensors. , 2017, Physical review letters.

[30]  Jes'us Rubio,et al.  Non-asymptotic analysis of quantum metrology protocols beyond the Cramér–Rao bound , 2017, 1707.05022.

[31]  Chun-Hua Yuan,et al.  Intramode-correlation-enhanced phase sensitivities in an SU(1,1) interferometer , 2016, 1609.03308.

[32]  L. Pezzè,et al.  Quantum metrology with nonclassical states of atomic ensembles , 2016, Reviews of Modern Physics.

[33]  Jing Liu,et al.  Valid lower bound for all estimators in quantum parameter estimation , 2016, 1609.01618.

[34]  Esteban Martinez,et al.  Quantum estimation of unknown parameters , 2016, 1606.07899.

[35]  E. Solano,et al.  Quantum Estimation Methods for Quantum Illumination. , 2016, Physical review letters.

[36]  Mankei Tsang,et al.  Quantum Weiss-Weinstein bounds for quantum metrology , 2015, 1511.08974.

[37]  Mankei Tsang,et al.  Quantum theory of superresolution for two incoherent optical point sources , 2015, 1511.00552.

[38]  Mankei Tsang,et al.  Quantum Bell-Ziv-Zakai Bounds and Heisenberg Limits for Waveform Estimation , 2014, 1409.7877.

[39]  Nicolas Gisin,et al.  Tighter quantum uncertainty relations following from a general probabilistic bound , 2014, 1409.4440.

[40]  J. Kołodyński,et al.  Quantum limits in optical interferometry , 2014, 1405.7703.

[41]  G. Tóth,et al.  Quantum metrology from a quantum information science perspective , 2014, 1405.4878.

[42]  Franco Nori,et al.  Enhanced interferometry using squeezed thermal states and even or odd states , 2014, 1405.2397.

[43]  Nicol'as Quesada,et al.  Quantum correlations in optical metrology: Heisenberg-limited phase estimation without mode entanglement , 2014, 1404.7110.

[44]  Jing Liu,et al.  Phase-matching condition for enhancement of phase sensitivity in quantum metrology , 2013, 1308.4799.

[45]  Carlos A. Pérez-Delgado,et al.  Fundamental limits of classical and quantum imaging. , 2012, Physical review letters.

[46]  Mankei Tsang,et al.  Ziv-Zakai error bounds for quantum parameter estimation. , 2011, Physical review letters.

[47]  Seth Lloyd,et al.  Quantum measurement bounds beyond the uncertainty relations. , 2011, Physical review letters.

[48]  Denes Petz,et al.  Extremal properties of the variance and the quantum Fisher information , 2011, 1109.2831.

[49]  S. Lloyd,et al.  Advances in quantum metrology , 2011, 1102.2318.

[50]  Rafal Demkowicz-Dobrzanski,et al.  Optimal phase estimation with arbitrary a priori knowledge , 2011, 1102.0786.

[51]  Carlton M. Caves,et al.  Fundamental quantum limit to waveform estimation , 2010, CLEO: 2011 - Laser Science to Photonic Applications.

[52]  Masahito Hayashi,et al.  Comparison Between the Cramer-Rao and the Mini-max Approaches in Quantum Channel Estimation , 2010, 1003.4575.

[53]  Alfredo Luis,et al.  Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes. , 2010, Physical review letters.

[54]  Aravind Chiruvelli,et al.  Quantum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit. , 2009, Physical review letters.

[55]  Yonina C. Eldar,et al.  A Lower Bound on the Bayesian MSE Based on the Optimal Bias Function , 2008, IEEE Transactions on Information Theory.

[56]  M. Paris.  Quantum estimation for quantum technology , 2008, 0804.2981.

[57]  G. Milburn,et al.  Quantum technology: the second quantum revolution , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[58]  Klauder,et al.  SU(2) and SU(1,1) interferometers. , 1986, Physical review. A, General physics.

[59]  Tzay Y. Young,et al.  Error bounds for stochastic estimation of signal parameters , 1971, IEEE Trans. Inf. Theory.

[60]  W. Marsden.  I and J , 2012 .

[61]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[62]  C. Helstrom.  Quantum detection and estimation theory , 1969 .