The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier trans...The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.展开更多
Quantum phase estimation reveals the power of quantum resources to beat the standard quantum limit and has been widely used in many fields.To improve the precision of phase estimation,we discuss the optimal probe stat...Quantum phase estimation reveals the power of quantum resources to beat the standard quantum limit and has been widely used in many fields.To improve the precision of phase estimation,we discuss the optimal probe states for phase estimation with a fixed mean particle number.By searching for the maximum quantum Fisher information,we optimize the probe states,which are superior to the path-entangled Fock states.Comparing the mean particle number(n)with the dimension of the probe states in Fock space(N+1),when n≤N,our optimal probe states can provide a better performance than the n00n states.When n>N,our optimal probe states can also remain optimal if the dimension of the probe states is large enough.展开更多
The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal q...The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.展开更多
Security and privacy issues have attracted the attention of researchers in the field of IoT as the information processing scale grows in sensor networks.Quantum computing,theoretically known as an absolutely secure wa...Security and privacy issues have attracted the attention of researchers in the field of IoT as the information processing scale grows in sensor networks.Quantum computing,theoretically known as an absolutely secure way to store and transmit information as well as a speed-up way to accelerate local or distributed classical algorithms that are hard to solve with polynomial complexity in computation or communication.In this paper,we focus on the phase estimation method that is crucial to the realization of a general multi-party computing model,which is able to be accelerated by quantum algorithms.A novel multi-party phase estimation algorithm and the related quantum circuit are proposed by using a distributed Oracle operator with iterations.The proved theoretical communication complexity of this algorithm shows it can give the phase estimation before applying multi-party computing efficiently without increasing any additional complexity.Moreover,a practical problem of multi-party dating investigated shows it can make a successful estimation of the number of solution in advance with zero communication complexity by utilizing its special statistic feature.Sufficient simulations present the correctness,validity and efficiency of the proposed estimation method.展开更多
Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in...Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in time-independent Hamiltonians.Here,our work makes an effort to explore multi-parameter estimation with time-dependent Hamiltonians.In particular,we focus on the discrimination of two close frequencies of a magnetic field by using a single qubit.We optimize the quantum controls by employing both traditional optimization methods and reinforcement learning to improve the precision for estimating the frequencies of the two magnetic fields.In addition to the estimation precision,we also evaluate the robustness of the optimization schemes against the shift of the control parameters.The results demonstrate that the hybrid reinforcement learning approach achieves the highest estimation precision,and exhibits superior robustness.Moreover,a fundamental challenge in multi-parameter quantum estimation stems from the incompatibility of the optimal control strategies for different parameters.We demonstrate that the hybrid control strategies derived through numerical optimization remain effective in enhancing the precision of multi-parameter estimation in spite of the incompatibilities,thereby mitigating incompatibilities between control strategies on the estimation precision.Finally,we investigate the trade-offs in estimation precision among different parameters for different scenarios,revealing the inherent challenges in balancing the optimization of multiple parameters simultaneously and providing insights into the fundamental distinction between quantum single-parameter estimation and multi-parameter estimation.展开更多
We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an op...We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach-Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer- Rao bound than the pure active （e.g., SU（1, I）） interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [Phys. Rev. D 23 1693 （1981）], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves＇ scheme.展开更多
We theoretically study the quantum Fisher information（QFI） of the SU（1,1） interferometer with phase shifts in two arms by coherent squeezed vacuum state input, and give the comparison with the result of phase shi...We theoretically study the quantum Fisher information（QFI） of the SU（1,1） interferometer with phase shifts in two arms by coherent squeezed vacuum state input, and give the comparison with the result of phase shift only in one arm.Different from the traditional Mach–Zehnder interferometer, the QFI of single-arm case for an SU（1,1） interferometer can be slightly higher or lower than that of two-arm case, which depends on the intensities of the two arms of the interferometer.For coherent squeezed vacuum state input with a fixed mean photon number, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.展开更多
Quantum multi-parameter estimation has recently attracted increased attention due to its wide applications, with a primary goal of designing high-precision measurement schemes for unknown parameters. While existing re...Quantum multi-parameter estimation has recently attracted increased attention due to its wide applications, with a primary goal of designing high-precision measurement schemes for unknown parameters. While existing research has predominantly concentrated on time-independent Hamiltonians, little has been known about quantum multi-parameter estimation for time-dependent Hamiltonians due to the complexity of quantum dynamics. This work bridges the gap by investigating the precision limit of multi-parameter quantum estimation for a qubit in an oscillating magnetic field model with multiple unknown frequencies. As the well-known quantum Cramer–Rao bound is generally unattainable due to the potential incompatibility between the optimal measurements for different parameters, we use the most informative bound instead which is always attainable and equivalent to the Holevo bound in the asymptotic limit. Moreover, we apply additional Hamiltonian to the system to engineer the dynamics of the qubit. By utilizing the quasi-Newton method, we explore the optimal schemes to attain the highest precision for the unknown frequencies of the magnetic field, including the simultaneous optimization of initial state preparation, the control Hamiltonian and the final measurement. The results indicate that the optimization can yield much higher precisions for the field frequencies than those without the optimizations. Finally,we study the robustness of the optimal control scheme with respect to the fluctuation of the interested frequencies, and the optimized scheme exhibits superior robustness to the scenario without any optimization.展开更多
We investigate phase estimation in a lossy interferometer using entangled coherent states,with a particular focus on a scenario where no reference beam is employed.By calculating the quantum Fisher information,we reve...We investigate phase estimation in a lossy interferometer using entangled coherent states,with a particular focus on a scenario where no reference beam is employed.By calculating the quantum Fisher information,we reveal two key results:(1)the metrological equivalence between scenarios with and without a reference beam,established under ideal lossless conditions for the two-phase-shifting configuration,breaks down in the presence of photon loss,and(2)the pronounced inferior performance of ECSs relative to NOON states,observed in the presence of a reference beam,disappears in its absence.展开更多
The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation,yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale ...The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation,yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum(NISQ)devices due to their excessive depth and circuit complexity.We demonstrate a high-precision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement.The iterative framework of the algorithm,combined with the independence from controlled unitary operations,inherently mitigates circuit depth and complexity limitations.Through an experimental realization on the photonic system,we demonstrate high-precision estimation of diverse phase differences,showing root-mean-square errors(RMSE)below the standard quantum limit𝒪(1/√N)and reaching the Heisenberg scaling𝒪(1/N)after a certain number of iterations.Our scheme provides a critical advantage in quantum resource-constrained scenarios,and advances practical implementations of quantum information tasks under realistic hardware constraints.展开更多
The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. ...The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts： measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters （e.g., squeezed state and quantum entanglement） yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are.展开更多
The dynamics of the quantum Fisher information(QFI) of phase parameter estimation in a non-Markovian dissipative qubit system is investigated within the structure of single and double Lorentzian spectra. We use the ti...The dynamics of the quantum Fisher information(QFI) of phase parameter estimation in a non-Markovian dissipative qubit system is investigated within the structure of single and double Lorentzian spectra. We use the time-convolutionless method with fourth-order perturbation expansion to obtain the general forms of QFI for the qubit system in terms of a non-Markovian master equation. We find that the phase parameter estimation can be enhanced in our model within both single and double Lorentzian spectra. What is more, the detuning and spectral width are two significant factors affecting the enhancement of parameter-estimation precision.展开更多
Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted ...Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.展开更多
We investigate the phase sensitivity of the SU（1,1） interfereometer [SU（1,1）I] and the modified Mach-Zehnder in- terferometer （MMZI） with the entangled coherent states （ECS） as inputs. We consider the ideal ca...We investigate the phase sensitivity of the SU（1,1） interfereometer [SU（1,1）I] and the modified Mach-Zehnder in- terferometer （MMZI） with the entangled coherent states （ECS） as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU（1,1）I can beat the shot-noise limit （SNL） and approach the Heisenberg limit （HL）. In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU（1,1）I, and the MMZI is more robust against internal photon losses than the SU（1,1）I.展开更多
We theoretically investigate the phase sensitivity with parity measurement on a Mach–Zehnder interferometer with a coherent state combined with a squeezed number state. Within a constraint on the total mean photon nu...We theoretically investigate the phase sensitivity with parity measurement on a Mach–Zehnder interferometer with a coherent state combined with a squeezed number state. Within a constraint on the total mean photon number, we find, via parity measurement, that the mixing of a coherent state and squeezed number state can give better phase sensitivity than mixing a coherent state and squeezed vacuum state when the phase shift deviates from the optimal phase φ= 0. In addition,we show that the classical Fisher information for parity measurement saturates the quantum Fisher information when the phase shift approaches to zero. Thus, the quantum Crame′r–Rao bound can be reached via the parity measurement in the case of φ= 0.展开更多
We investigate the sensitivity of phase estimation in a Mach-Zehnder interferometer with photon-subtracted twomode squeezed vacuum states.Our results show that, for given initial squeezing parameter, both symmetric an...We investigate the sensitivity of phase estimation in a Mach-Zehnder interferometer with photon-subtracted twomode squeezed vacuum states.Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér-Rao bound(i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction.On the other hand, the quantum Cramér-Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states.In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse.Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.展开更多
We derive a general phase-matching condition(PMC) for enhancement of sensitivity in SU(1,1) interferometers. Under this condition, the quantum Fisher information(QFI) of two-mode SU(1,1) interferometry becomes maximal...We derive a general phase-matching condition(PMC) for enhancement of sensitivity in SU(1,1) interferometers. Under this condition, the quantum Fisher information(QFI) of two-mode SU(1,1) interferometry becomes maximal with respect to the relative phase of two modes, for the case of an arbitrary state in one input port and an even(odd) state in the other port, and the phase sensitivity is enhanced. We also find that optimal parameters can let the QFI in some areas achieve the Heisenberg limit for both pure and mixed initial states. As examples, we consider several input states: coherent and even coherent states, squeezed vacuum and even coherent states, squeezed thermal and even coherent states. Furthermore, in the realistic scenario of the photon loss channel, we investigate the effect of photon losses on QFI with numerical studies. We find the PMC remains unchanged and is not affected by the transmission coefficients for the above input states. Our results suggest that the PMC can exist in various kinds of interferometers and the phase-matching is robust to even strong photon losses.展开更多
The Mach-Zehnder interferometer is a fundamental tool for measuring phase shifts between two light paths,serving as a crucial prototype for achieving high-precision measurements in various scientific and technological...The Mach-Zehnder interferometer is a fundamental tool for measuring phase shifts between two light paths,serving as a crucial prototype for achieving high-precision measurements in various scientific and technological applications.In this study,we analyze different models for estimating the relative phase shift in a general two-arm Mach-Zehnder interferometer.We demonstrated that single-parameter estimation models can be reduced from the two-parameter estimation model by imposing appropriate constraints on the parameter space.To make quantum Fisher information of the single-parameter estimation models meaningful,the corresponding constraints must be guaranteed in the experiment implementation.Furthermore,we apply the quantum Fisher information approach to analyze the Mach-Zehnder interferometer with the an input state composed of a displaced squeezed vacuum state and a coherent state,providing insights into the precision limits of such configurations.展开更多
基金Supported by the National Natural Science Foundation of China Grant No.10874098the National Basic Research Program of China under Grant Nos.2009CB929402 and 2011CB9216002
文摘The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.
基金supported by the National Natural Science Foundation of China(Grant No.12405026)the Natural Science Foundation of Hangzhou(Grant No.2024SZRYBA050001)。
文摘Quantum phase estimation reveals the power of quantum resources to beat the standard quantum limit and has been widely used in many fields.To improve the precision of phase estimation,we discuss the optimal probe states for phase estimation with a fixed mean particle number.By searching for the maximum quantum Fisher information,we optimize the probe states,which are superior to the path-entangled Fock states.Comparing the mean particle number(n)with the dimension of the probe states in Fock space(N+1),when n≤N,our optimal probe states can provide a better performance than the n00n states.When n>N,our optimal probe states can also remain optimal if the dimension of the probe states is large enough.
基金supported by the National Natural Science Foundation of China(Grants No.11247294)the Research Foundation of Education Bureau of Hunan Province,China(Grant No.12C0826)+2 种基金the Doctor Foundation Startup from Hunan University of Arts and Science,China(Grant No.13101039)the Key Laboratory of Photoelectricity Information Integration and Optics Manufacture Technology in Hunan Province,Chinathe Construct Program of the Key Discipline in Hunan University of Arts and Science(Optics),China
文摘The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement （WM） and quantum measurement reversal （QMR）. We derive the exact expressions of the optimal quantum Fisher information （QFI） and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61501247,61373131 and 61702277,the Six Talent Peaks Project of Jiangsu Province(Grant No.2015-XXRJ-013)Natural Science Foundation of Jiangsu Province(Grant No.BK20171458)+3 种基金the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province(China under Grant No.16KJB520030)the NUIST Research Foundation for Talented Scholars under Grant Nos.2015r014,PAPD and CICAEET fundsfunded in part by the Science and Technology Development Fund,Macao SAR(File No.SKL-IOTSC-2018-2020,0018/2019/AKP,0008/2019/AGJ,and FDCT/194/2017/A3)in part by the University of Macao under Grant Nos.MYRG2018-00248-FST and MYRG2019-0137-FST.
文摘Security and privacy issues have attracted the attention of researchers in the field of IoT as the information processing scale grows in sensor networks.Quantum computing,theoretically known as an absolutely secure way to store and transmit information as well as a speed-up way to accelerate local or distributed classical algorithms that are hard to solve with polynomial complexity in computation or communication.In this paper,we focus on the phase estimation method that is crucial to the realization of a general multi-party computing model,which is able to be accelerated by quantum algorithms.A novel multi-party phase estimation algorithm and the related quantum circuit are proposed by using a distributed Oracle operator with iterations.The proved theoretical communication complexity of this algorithm shows it can give the phase estimation before applying multi-party computing efficiently without increasing any additional complexity.Moreover,a practical problem of multi-party dating investigated shows it can make a successful estimation of the number of solution in advance with zero communication complexity by utilizing its special statistic feature.Sufficient simulations present the correctness,validity and efficiency of the proposed estimation method.
基金supported by the National Natural Science Foundation of China(Grant No.12075323)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0300702).
文摘Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in time-independent Hamiltonians.Here,our work makes an effort to explore multi-parameter estimation with time-dependent Hamiltonians.In particular,we focus on the discrimination of two close frequencies of a magnetic field by using a single qubit.We optimize the quantum controls by employing both traditional optimization methods and reinforcement learning to improve the precision for estimating the frequencies of the two magnetic fields.In addition to the estimation precision,we also evaluate the robustness of the optimization schemes against the shift of the control parameters.The results demonstrate that the hybrid reinforcement learning approach achieves the highest estimation precision,and exhibits superior robustness.Moreover,a fundamental challenge in multi-parameter quantum estimation stems from the incompatibility of the optimal control strategies for different parameters.We demonstrate that the hybrid control strategies derived through numerical optimization remain effective in enhancing the precision of multi-parameter estimation in spite of the incompatibilities,thereby mitigating incompatibilities between control strategies on the estimation precision.Finally,we investigate the trade-offs in estimation precision among different parameters for different scenarios,revealing the inherent challenges in balancing the optimization of multiple parameters simultaneously and providing insights into the fundamental distinction between quantum single-parameter estimation and multi-parameter estimation.
基金Project supported by the National Natural Science Foundation of China(Grant No.11665010)the Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education,China(Grant No.QSQC1414)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.17B055)
文摘We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach-Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer- Rao bound than the pure active （e.g., SU（1, I）） interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [Phys. Rev. D 23 1693 （1981）], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves＇ scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11474095,11654005,and 11234003)the National Key Research and Development Program of China(Grant No.2016YFA0302000)
文摘We theoretically study the quantum Fisher information（QFI） of the SU（1,1） interferometer with phase shifts in two arms by coherent squeezed vacuum state input, and give the comparison with the result of phase shift only in one arm.Different from the traditional Mach–Zehnder interferometer, the QFI of single-arm case for an SU（1,1） interferometer can be slightly higher or lower than that of two-arm case, which depends on the intensities of the two arms of the interferometer.For coherent squeezed vacuum state input with a fixed mean photon number, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12075323)。
文摘Quantum multi-parameter estimation has recently attracted increased attention due to its wide applications, with a primary goal of designing high-precision measurement schemes for unknown parameters. While existing research has predominantly concentrated on time-independent Hamiltonians, little has been known about quantum multi-parameter estimation for time-dependent Hamiltonians due to the complexity of quantum dynamics. This work bridges the gap by investigating the precision limit of multi-parameter quantum estimation for a qubit in an oscillating magnetic field model with multiple unknown frequencies. As the well-known quantum Cramer–Rao bound is generally unattainable due to the potential incompatibility between the optimal measurements for different parameters, we use the most informative bound instead which is always attainable and equivalent to the Holevo bound in the asymptotic limit. Moreover, we apply additional Hamiltonian to the system to engineer the dynamics of the qubit. By utilizing the quasi-Newton method, we explore the optimal schemes to attain the highest precision for the unknown frequencies of the magnetic field, including the simultaneous optimization of initial state preparation, the control Hamiltonian and the final measurement. The results indicate that the optimization can yield much higher precisions for the field frequencies than those without the optimizations. Finally,we study the robustness of the optimal control scheme with respect to the fluctuation of the interested frequencies, and the optimized scheme exhibits superior robustness to the scenario without any optimization.
基金supported by the NSFC through Grant No.12005106the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.JSCX23-0260)Natural Science Foundation of Nanjing University of Posts and Telecommunications(Grant No.NY224127)。
文摘We investigate phase estimation in a lossy interferometer using entangled coherent states,with a particular focus on a scenario where no reference beam is employed.By calculating the quantum Fisher information,we reveal two key results:(1)the metrological equivalence between scenarios with and without a reference beam,established under ideal lossless conditions for the two-phase-shifting configuration,breaks down in the presence of photon loss,and(2)the pronounced inferior performance of ECSs relative to NOON states,observed in the presence of a reference beam,disappears in its absence.
基金Project supported by the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20233001 and BK20243060)the National Natural Science Foundation of China(Grant No.62288101)。
文摘The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation,yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum(NISQ)devices due to their excessive depth and circuit complexity.We demonstrate a high-precision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement.The iterative framework of the algorithm,combined with the independence from controlled unitary operations,inherently mitigates circuit depth and complexity limitations.Through an experimental realization on the photonic system,we demonstrate high-precision estimation of diverse phase differences,showing root-mean-square errors(RMSE)below the standard quantum limit𝒪(1/√N)and reaching the Heisenberg scaling𝒪(1/N)after a certain number of iterations.Our scheme provides a critical advantage in quantum resource-constrained scenarios,and advances practical implementations of quantum information tasks under realistic hardware constraints.
基金Project supported by the National Basic Research Program of China(Grant Nos.2011CBA00200 and 2011CB9211200)the National Natural Science Foun-dation of China(Grant Nos.61108009 and 61222504)+1 种基金the Anhui Provincial Natural Science Foundation,China(Grant No.1208085QA08)the Ph.D.Program Foundation of Ministry of Education of China(Grant No.20113402120017)
文摘The statistical error is ineluctable in any measurement. Quantum techniques, especially with the development of quantum information, can help us squeeze the statistical error and enhance the precision of measurement. In a quantum system, there are some quantum parameters, such as the quantum state, quantum operator, and quantum dimension, which have no classical counterparts. So quantum metrology deals with not only the traditional parameters, but also the quantum parameters. Quantum metrology includes two important parts： measuring the physical parameters with a precision beating the classical physics limit and measuring the quantum parameters precisely. In this review, we will introduce how quantum characters （e.g., squeezed state and quantum entanglement） yield a higher precision, what the research areas are scientists most interesting in, and what the development status of quantum metrology and its perspectives are.
基金Projects supported by the Natural Science Foundation of Guangdong Province,China(Grant No.2015A030310354)the Science Foundation for Enhancing School with Innovation of Guangdong Ocean University(Grant Nos.GDOU2017052504 and GDOU2015050207)+1 种基金the Foundation of Excellent-YoungBackbone Teacher of Guangdong Ocean University(Grant No.HDYQ2017005)the Fund of University Student Innovation and Entrepreneurship Team of Guangdong Ocean University(Grant No.CCTD201823)
文摘The dynamics of the quantum Fisher information(QFI) of phase parameter estimation in a non-Markovian dissipative qubit system is investigated within the structure of single and double Lorentzian spectra. We use the time-convolutionless method with fourth-order perturbation expansion to obtain the general forms of QFI for the qubit system in terms of a non-Markovian master equation. We find that the phase parameter estimation can be enhanced in our model within both single and double Lorentzian spectra. What is more, the detuning and spectral width are two significant factors affecting the enhancement of parameter-estimation precision.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 92065113, 11904357, 62075208, and 12174367)the Innovation Programme for Quantum Science and Technology (Grant No. 2021ZD0301604)+1 种基金the National Key Research and Development Program of China (Grant No. 2021YFE0113100)supported by Beijing Academy of Quantum Information Sciences
文摘Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.
基金supported by the Major Research Plan of the National Natural Science Foundation of China(Grant No.91121023)the National Natural Science Foundation of China(Grant Nos.11574092,61378012,and 60978009)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20124407110009)the National Basic Research Program of China(Grant Nos.2011CBA00200 and 2013CB921804)the Program for Innovative Research Team in University(Grant No.IRT1243)
文摘We investigate the phase sensitivity of the SU（1,1） interfereometer [SU（1,1）I] and the modified Mach-Zehnder in- terferometer （MMZI） with the entangled coherent states （ECS） as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU（1,1）I can beat the shot-noise limit （SNL） and approach the Heisenberg limit （HL）. In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU（1,1）I, and the MMZI is more robust against internal photon losses than the SU（1,1）I.
基金Project supported by the National Natural Science Foundation of China(Grant No.11404040)the Qing Lan Project of the Higher Educations of Jiangsu Province of China
文摘We theoretically investigate the phase sensitivity with parity measurement on a Mach–Zehnder interferometer with a coherent state combined with a squeezed number state. Within a constraint on the total mean photon number, we find, via parity measurement, that the mixing of a coherent state and squeezed number state can give better phase sensitivity than mixing a coherent state and squeezed vacuum state when the phase shift deviates from the optimal phase φ= 0. In addition,we show that the classical Fisher information for parity measurement saturates the quantum Fisher information when the phase shift approaches to zero. Thus, the quantum Crame′r–Rao bound can be reached via the parity measurement in the case of φ= 0.
基金Project supported by the National Natural Science Foundation of China(Grant No.11404040)the Qing Lan Project of the Higher Educations of Jiangsu Province of China
文摘We investigate the sensitivity of phase estimation in a Mach-Zehnder interferometer with photon-subtracted twomode squeezed vacuum states.Our results show that, for given initial squeezing parameter, both symmetric and asymmetric photon subtractions can further improve the quantum Cramér-Rao bound(i.e., the ultimate phase sensitivity), especially for single-mode photon subtraction.On the other hand, the quantum Cramér-Rao bound can be reached by parity detection for symmetric photon-subtracted two-mode squeezed vacuum states at particular values of the phase shift, but it is not valid for asymmetric photon-subtracted two-mode squeezed vacuum states.In addition, compared with the two-mode squeezed vacuum state, the phase sensitivity via parity detection with asymmetric photon-subtracted two-mode squeezed vacuum states will be getting worse.Thus, parity detection may not always be the optimal detection scheme for nonclassical states of light when they are considered as the interferometer states.
基金Supported by the National Key Research and Development Program of China under Grant Nos.2017YFA0304202 and 2017YFA0205700the NSFC through Grant No.11875231the Fundamental Research Funds for the Central Universities through Grant No.2018FZA3005
文摘We derive a general phase-matching condition(PMC) for enhancement of sensitivity in SU(1,1) interferometers. Under this condition, the quantum Fisher information(QFI) of two-mode SU(1,1) interferometry becomes maximal with respect to the relative phase of two modes, for the case of an arbitrary state in one input port and an even(odd) state in the other port, and the phase sensitivity is enhanced. We also find that optimal parameters can let the QFI in some areas achieve the Heisenberg limit for both pure and mixed initial states. As examples, we consider several input states: coherent and even coherent states, squeezed vacuum and even coherent states, squeezed thermal and even coherent states. Furthermore, in the realistic scenario of the photon loss channel, we investigate the effect of photon losses on QFI with numerical studies. We find the PMC remains unchanged and is not affected by the transmission coefficients for the above input states. Our results suggest that the PMC can exist in various kinds of interferometers and the phase-matching is robust to even strong photon losses.
基金supported by the National Natural Science Foundation of China(Grants Nos.92476118 and 12275062).
文摘The Mach-Zehnder interferometer is a fundamental tool for measuring phase shifts between two light paths,serving as a crucial prototype for achieving high-precision measurements in various scientific and technological applications.In this study,we analyze different models for estimating the relative phase shift in a general two-arm Mach-Zehnder interferometer.We demonstrated that single-parameter estimation models can be reduced from the two-parameter estimation model by imposing appropriate constraints on the parameter space.To make quantum Fisher information of the single-parameter estimation models meaningful,the corresponding constraints must be guaranteed in the experiment implementation.Furthermore,we apply the quantum Fisher information approach to analyze the Mach-Zehnder interferometer with the an input state composed of a displaced squeezed vacuum state and a coherent state,providing insights into the precision limits of such configurations.
