The maximum entangled number state （NOON state） can improve the sensitivity of physical quantity measure- ment to the Heisenberg limit 1/N. In this work, the magnetic field measurement based on the individual solid ...The maximum entangled number state （NOON state） can improve the sensitivity of physical quantity measure- ment to the Heisenberg limit 1/N. In this work, the magnetic field measurement based on the individual solid spin NOON state is investigated. Based on the tunable effective coupling coefficient, we propose a generation scheme of the three-spin NOON state, i.e, the Creenberger-Horne-Zeilinger （CHZ） state, and discussed the mea- surement resolution reduction due to decoherence. It is unnecessary to entangle spins as many as possible when decoherence exists. In practice, defect spins in diamond and alp donors with long coherence time can be applied with current techniques in the nano-scaled high resolution magnetic measurement.展开更多
Dynamical decoupling(DD)is normally ineffective when applied to DC measurement.In its straightforward implementation,DD nulls out DC signal as well while suppressing noise.This work proposes a phase relay method that ...Dynamical decoupling(DD)is normally ineffective when applied to DC measurement.In its straightforward implementation,DD nulls out DC signal as well while suppressing noise.This work proposes a phase relay method that is capable of continuously interrogating the DC signal over many DD cycles.We illustrate its efficacy when applied to the measurement of a weak DC magnetic field with an atomic spinor Bose-Einstein condensate.Sensitivities approaching standard quantum limit or Heisenberg limit are potentially realizable for a coherent spin state or a squeezed spin state of 10000 atoms,respectively,while ambient laboratory level noise is suppressed by DD.Our work offers a practical approach to mitigate the limitations of DD to DC measurement and would find other applications for resorting coherence in quantum sensing and quantum information processing research.展开更多
Sagnac effect enhancement can improve optical gyro precision. For a certain input intensity, we suggest that the other input port of beam splitter（BS） should be fed with some quantum light to break through shot nois...Sagnac effect enhancement can improve optical gyro precision. For a certain input intensity, we suggest that the other input port of beam splitter（BS） should be fed with some quantum light to break through shot noise limit（SNL） to improve Sagnac effect without increasing radiation-pressure noise（NRP）. We design a Sagnac effect quantum enhancement criterion（SQEC） to judge whether some quantum light can enhance Sagnac effect and present a Sagnac effect enhancement scheme that utilizing Fock state light and parity measurement technique to extract the output phase. The results of the theoretical analysis show that the maximum sensitivity can be reached at θ = 0, and the phase precision can break through SNL and even achieve Heisenberg limit（HL）. When the Fock state average photon number n is far less than coherent state, the minimum measurable angular rate is improved with √2n＋1 times, which can deduce shot noise and increase NRP little.展开更多
SU(1,1) interferometers play an important role in quantum metrology. Previous studies focus on various inputs and detection strategies with symmetric gain. In this paper, we analyze a modified SU(1,1) interferometer u...SU(1,1) interferometers play an important role in quantum metrology. Previous studies focus on various inputs and detection strategies with symmetric gain. In this paper, we analyze a modified SU(1,1) interferometer using asymmetric gain. Two vacuum states are used as the input and on–off detection is performed at the output. In a lossless scenario,symmetric gain is the optimal selection and the corresponding phase sensitivity can achieve the Heisenberg limit as well as the quantum Cramer–Rao bound. In addition, we analyze the phase sensitivity with symmetric gain in the lossy scenario.The phase sensitivity is sensitive to internal losses but extremely robust against external losses. We address the optimal asymmetric gain and the results suggest that this method can improve the tolerance to internal losses. Our work may contribute to the practical development of quantum metrology.展开更多
Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it i...Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In 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 parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For 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.展开更多
In the present study, time evolution of quantum Cramer–Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dy...In the present study, time evolution of quantum Cramer–Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.展开更多
Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finit...Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as Clifford + T. Although these logical gate sets allow for universal quantum computation, the finite gate sizes present a problem for quantum sensing, since in sensing protocols, such as the Ramsey measurement protocol, the signal must act continuously. The difficulty in constructing a continuous logical op-erator comes from the Eastin-Knill theorem, which prevents a continuous sig-nal from being both fault-tolerant to local errors and transverse. Since error correction is needed to approach the Heisenberg Limit in a noisy environment, it is important to explore how to construct fault-tolerant continuous operators. In this paper, a protocol to design continuous logical z-rotations is proposed and applied to the Steane Code. The fault tolerance of the designed operator is investigated using the Knill-Laflamme conditions. The Knill-Laflamme condi-tions indicate that the diagonal unitary operator constructed cannot be fault tolerant solely due to the possibilities of X errors on the middle qubit. The ap-proach demonstrated throughout this paper may, however, find success in codes with more qubits such as the Shor code, distance 3 surface code, [15, 1, 3] code, or codes with a larger distance such as the [11, 1, 5] code.展开更多
Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superre...Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O（M/N2）, where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i） an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii） a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N2, and iii） a protocol that generates O（N2） nearly perfect copies of a generic pure state U｜0） while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M2/N2.展开更多
基金Supported by the National Basic Research Program of China(No 2011CB921200)the Strategic Priority Research Program(B)of the Chinese Academy of Sciences under Grant (No XDB01030200)+1 种基金the National Natural Science Foundation of China(No11374290)the Fundamental Research Funds for the Central Universities and the Foundation for Authors of National Excellent Doctoral Dissertation of China
文摘The maximum entangled number state （NOON state） can improve the sensitivity of physical quantity measure- ment to the Heisenberg limit 1/N. In this work, the magnetic field measurement based on the individual solid spin NOON state is investigated. Based on the tunable effective coupling coefficient, we propose a generation scheme of the three-spin NOON state, i.e, the Creenberger-Horne-Zeilinger （CHZ） state, and discussed the mea- surement resolution reduction due to decoherence. It is unnecessary to entangle spins as many as possible when decoherence exists. In practice, defect spins in diamond and alp donors with long coherence time can be applied with current techniques in the nano-scaled high resolution magnetic measurement.
基金Project supported by the NSAF(Grant No.U1930201)the National Natural Science Foundation of China(Grant Nos.12274331,91836101,and 91836302)+1 种基金the National Key R&D Program of China(Grant No.2018YFA0306504)Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302100).
文摘Dynamical decoupling(DD)is normally ineffective when applied to DC measurement.In its straightforward implementation,DD nulls out DC signal as well while suppressing noise.This work proposes a phase relay method that is capable of continuously interrogating the DC signal over many DD cycles.We illustrate its efficacy when applied to the measurement of a weak DC magnetic field with an atomic spinor Bose-Einstein condensate.Sensitivities approaching standard quantum limit or Heisenberg limit are potentially realizable for a coherent spin state or a squeezed spin state of 10000 atoms,respectively,while ambient laboratory level noise is suppressed by DD.Our work offers a practical approach to mitigate the limitations of DD to DC measurement and would find other applications for resorting coherence in quantum sensing and quantum information processing research.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61573372 and 61603413)
文摘Sagnac effect enhancement can improve optical gyro precision. For a certain input intensity, we suggest that the other input port of beam splitter（BS） should be fed with some quantum light to break through shot noise limit（SNL） to improve Sagnac effect without increasing radiation-pressure noise（NRP）. We design a Sagnac effect quantum enhancement criterion（SQEC） to judge whether some quantum light can enhance Sagnac effect and present a Sagnac effect enhancement scheme that utilizing Fock state light and parity measurement technique to extract the output phase. The results of the theoretical analysis show that the maximum sensitivity can be reached at θ = 0, and the phase precision can break through SNL and even achieve Heisenberg limit（HL）. When the Fock state average photon number n is far less than coherent state, the minimum measurable angular rate is improved with √2n＋1 times, which can deduce shot noise and increase NRP little.
基金Project supported by Leading Innovative Talents in Changzhou (Grant No.CQ20210107)Shuangchuang Ph.D Award (Grant No.JSSCBS20210915)+1 种基金Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No.21KJB140007)the National Natural Science Foundation of China (Grant No.12104193)。
文摘SU(1,1) interferometers play an important role in quantum metrology. Previous studies focus on various inputs and detection strategies with symmetric gain. In this paper, we analyze a modified SU(1,1) interferometer using asymmetric gain. Two vacuum states are used as the input and on–off detection is performed at the output. In a lossless scenario,symmetric gain is the optimal selection and the corresponding phase sensitivity can achieve the Heisenberg limit as well as the quantum Cramer–Rao bound. In addition, we analyze the phase sensitivity with symmetric gain in the lossy scenario.The phase sensitivity is sensitive to internal losses but extremely robust against external losses. We address the optimal asymmetric gain and the results suggest that this method can improve the tolerance to internal losses. Our work may contribute to the practical development of quantum metrology.
基金Project supported by the National Natural Science Foundation of China(Grant No.61873251)。
文摘Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In 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 parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For 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.
文摘In the present study, time evolution of quantum Cramer–Rao bound of entangled N00N state, as phase sensitivity, is determined by the aid of quantum estimation theory in the presence decoherence channels. Also, the dynamic quantum process as decoherence approach is characterized by quantum fisher information flow and entanglement amount in order to distinguish between Markovian and Non-Markovian process. The comparison between quantum fisher information and quantum fisher information flow assists to comprehend the phase sensitivity evolution corresponding to Non-Markovian and Markovian process. Furthermore, as result of backflow of information from the environment to system, the phase sensitivity corresponding memory effect of environment are revived after complete decay and increase in the few times.
文摘Error correction has long been suggested to extend the sensitivity of quantum sensors into the Heisenberg Limit. However, operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as Clifford + T. Although these logical gate sets allow for universal quantum computation, the finite gate sizes present a problem for quantum sensing, since in sensing protocols, such as the Ramsey measurement protocol, the signal must act continuously. The difficulty in constructing a continuous logical op-erator comes from the Eastin-Knill theorem, which prevents a continuous sig-nal from being both fault-tolerant to local errors and transverse. Since error correction is needed to approach the Heisenberg Limit in a noisy environment, it is important to explore how to construct fault-tolerant continuous operators. In this paper, a protocol to design continuous logical z-rotations is proposed and applied to the Steane Code. The fault tolerance of the designed operator is investigated using the Knill-Laflamme conditions. The Knill-Laflamme condi-tions indicate that the diagonal unitary operator constructed cannot be fault tolerant solely due to the possibilities of X errors on the middle qubit. The ap-proach demonstrated throughout this paper may, however, find success in codes with more qubits such as the Shor code, distance 3 surface code, [15, 1, 3] code, or codes with a larger distance such as the [11, 1, 5] code.
文摘Although the no-cloning theorem forbids perfect replication of quantum information, it is sometimes possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can occur for both quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication and provide a unified view of existing results. The paper also includes new results. In particular, we show that when quantum superreplication can be achieved, it can be achieved through estimation up to an error of size O（M/N2）, where N and M are the number of input and output copies, respectively. Quantum strategies still offer an advantage for superreplication in that they allow for exponentially faster reduction of the error. Using the relation with estimation, we provide i） an alternative proof of the optimality of Heisenberg scaling in quantum metrology, ii） a strategy for estimating arbitrary unitary gates with a mean square error scaling as log N/N2, and iii） a protocol that generates O（N2） nearly perfect copies of a generic pure state U｜0） while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M2/N2.
