In quantum metrology we usually extract information from the reduced probe system but ignore the information lost inevitably into the environment. However, K. Mφlmer [Phys. Rev. Lett. 114, 040401 （2015）] showed tha...In quantum metrology we usually extract information from the reduced probe system but ignore the information lost inevitably into the environment. However, K. Mφlmer [Phys. Rev. Lett. 114, 040401 （2015）] showed that the information lost into the environment has an important effect on improving the successful probability of quantum process discrimination. Here we reconsider the model of a driven atom coupled to an environment and distinguish which of two candidate Hamiltonians governs the dynamics of the whole system. We mainly discuss two measurement methods, one of which obtains only the information from the reduced atom state and the other obtains the information from both the atom and its environment. Interestingly, for the two methods the optimal initial states of the atom, used to improve the successful probability of the process discrimination, are different. By comparing the two methods we find that the partial information from the environment is very useful for the discriminations.展开更多
Extracting more information and saving quantum resources are two main aims for quantum measurements.However,the optimization of strategies for these two objectives varies when discriminating between quantum states |ψ...Extracting more information and saving quantum resources are two main aims for quantum measurements.However,the optimization of strategies for these two objectives varies when discriminating between quantum states |ψ_(0)> and |ψ_(1)> through multiple measurements.In this study,we introduce a novel state discrimination model that reveals the intricate relationship between the average error rate and average copy consumption.By integrating these two crucial metrics and minimizing their weighted sum for any given weight value,our research underscores the infeasibility of simultaneously minimizing these metrics through local measurements with one-way communication.Our findings present a compelling trade-off curve,highlighting the advantages of achieving a balance between error rate and copy consumption in quantum discrimination tasks,offering valuable insights into the optimization of quantum resources while ensuring the accuracy of quantum state discrimination.展开更多
In this paper, we present a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states in terms of the multiple-rail and polarization representation of a single photon. In our sche...In this paper, we present a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states in terms of the multiple-rail and polarization representation of a single photon. In our scheme, discriminated quantum states are expressed by using the spatial degree of freedom of a single photon while the polarization degree of freedom of the single photon is used to act as an auxiliary qubit. The optical components used in our scheme are only passive linear optical elements such as polarizing beam splitters, wave plates, polarizers, single photon detectors, and single photon source.展开更多
In this paper,we study the problem of sampling complexity for channel discrimination with respect to two different strategies:product strategy and adaptive strategy.We first formally introduce the definitions of the s...In this paper,we study the problem of sampling complexity for channel discrimination with respect to two different strategies:product strategy and adaptive strategy.We first formally introduce the definitions of the sampling complexity of the channels under the framework of hypothesis testing,wherein the goal is to determine the minimum number of samples needed to reach a desired error probability.We then establish the lower and upper bounds on the sampling complexity of the symmetric,asymmetric,and error exponent hypothesis testing settings.We show that,by imposing product strategy on testing,the bounds are always characterized by the generalized channel divergence,while with adaptive strategy,the bounds are characterized by the amortized channel divergence.Finally,we analyze two concrete examples,and obtain that the adaptive strategy can not lead to an advantage to the problem of determining the sampling complexity for classical-quantum channels,which can bring advantages for generalized amplitude damping channels.展开更多
We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of ...We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems,the results presented here show that this property is no longer true in tripartite systems.Furthermore,we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination,that is,we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement.Lastly,we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence.It is interesting that the frozen phenomenon exists for geometric discord in this scenario.展开更多
In this paper, we consider the minimax strategy to unambiguously discriminate two pure nonorthogonal quantum states without knowing a priori probability. By exploiting the positive-operator valued measure, we derive t...In this paper, we consider the minimax strategy to unambiguously discriminate two pure nonorthogonal quantum states without knowing a priori probability. By exploiting the positive-operator valued measure, we derive the upper bound of the minimax measurement of the optimal unambiguous state discrimination. Based on the linear optical devices, we propose an experimentally feasible scheme to implement a minimax measure of a general pair of two nonorthogonal quantum states.展开更多
Probabilistic quantum cloning（PQC） cannot copy a set of linearly dependent quantum states.In this paper,we show that if incorrect copies are allowed to be produced,linearly dependent quantum states may also be clone...Probabilistic quantum cloning（PQC） cannot copy a set of linearly dependent quantum states.In this paper,we show that if incorrect copies are allowed to be produced,linearly dependent quantum states may also be cloned by the PQC.By exploiting this kind of PQC to clone a special set of three linearly dependent quantum states,we derive the upper bound of the maximum confidence measure of a set.An explicit transformation of the maximum confidence measure is presented.展开更多
In this paper, we study the problem of multicopy quantum two-state discrimination. By exploring the quantum hypothesis testing, i.e., the probabilisfic quantum cloning, we derive the upper bounds of the minimal error ...In this paper, we study the problem of multicopy quantum two-state discrimination. By exploring the quantum hypothesis testing, i.e., the probabilisfic quantum cloning, we derive the upper bounds of the minimal error discrimination （MED） and the optimal unambiguous discrimination （OUD）, which coincides with the Helstrom theorem and the JS limit. Furthermore, when prior probabilities are unknown, we derive the minimax MED and the minimax OUD. Based on the optimal NM probabilistic quantum cloning, we present the optimal strategies of collective measurements of the MED and the OUD. When the number of the copies is infinite, regardless of whether prior probabilities are known or not, the success probabilities of the MED and the OUD go to 100%, in accordance with the quantum measurement hypothesis that unknown quantum state can be determined if and only if infinite identical quantum state copies are given.展开更多
Quantum computing is a significant computing capability which is superior to classical computing because of its superposition feature. Distinguishing several quantum states from quantum algorithm outputs is often a vi...Quantum computing is a significant computing capability which is superior to classical computing because of its superposition feature. Distinguishing several quantum states from quantum algorithm outputs is often a vital computational task. In most cases, the quantum states tend to be non-orthogonal due to superposition; quantum mechanics has proved that perfect outcomes could not be achieved by measurements, forcing repetitive measurement. Hence, it is important to determine the optimum measuring method which requires fewer repetitions and a lower error rate. However, extending current measurement approaches mainly aiming at quantum cryptography to multi-qubit situations for quantum computing confronts challenges, such as conducting global operations which has considerable costs in the experimental realm. Therefore, in this study, we have proposed an optimum subsystem method to avoid these difficulties. We have provided an analysis of the comparison between the reduced subsystem method and the global minimum error method for two-qubit problems; the conclusions have been verified experimentally. The results showed that the subsystem method could effectively discriminate non-orthogonal two-qubit states, such as separable states, entangled pure states, and mixed states; the cost of the experimental process had been significantly reduced, in most circumstances, with acceptable error rate. We believe the optimal subsystem method is the most valuable and promising approach for multi-qubit quantum computing applications.展开更多
We exploit optimal probabilistic cloning to rederive the JS limit.Dependent on the formulation given by the optimal probabilistic cloning,the explicit transformation of a measure of the JS limit is presented.Based on ...We exploit optimal probabilistic cloning to rederive the JS limit.Dependent on the formulation given by the optimal probabilistic cloning,the explicit transformation of a measure of the JS limit is presented.Based on linear optical devices,we propose an experimentally feasible scheme to implement the JS limit measure of a general pair of two nonorthogonal quantum states.The success probability of the proposed scheme is unity.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11274043,11375025,and 11005008)
文摘In quantum metrology we usually extract information from the reduced probe system but ignore the information lost inevitably into the environment. However, K. Mφlmer [Phys. Rev. Lett. 114, 040401 （2015）] showed that the information lost into the environment has an important effect on improving the successful probability of quantum process discrimination. Here we reconsider the model of a driven atom coupled to an environment and distinguish which of two candidate Hamiltonians governs the dynamics of the whole system. We mainly discuss two measurement methods, one of which obtains only the information from the reduced atom state and the other obtains the information from both the atom and its environment. Interestingly, for the two methods the optimal initial states of the atom, used to improve the successful probability of the process discrimination, are different. By comparing the two methods we find that the partial information from the environment is very useful for the discriminations.
基金supported by the Fundamental Research Funds for the Central Universities(WK2470000035)USTC Research Funds of the Double First-Class Initiative(YD2030002007,YD2030002011)+1 种基金the National Natural Science Foundation of China(62222512,12104439,12134014,and 11974335)the Anhui Provincial Natural Science Foundation(2208085J03).
文摘Extracting more information and saving quantum resources are two main aims for quantum measurements.However,the optimization of strategies for these two objectives varies when discriminating between quantum states |ψ_(0)> and |ψ_(1)> through multiple measurements.In this study,we introduce a novel state discrimination model that reveals the intricate relationship between the average error rate and average copy consumption.By integrating these two crucial metrics and minimizing their weighted sum for any given weight value,our research underscores the infeasibility of simultaneously minimizing these metrics through local measurements with one-way communication.Our findings present a compelling trade-off curve,highlighting the advantages of achieving a balance between error rate and copy consumption in quantum discrimination tasks,offering valuable insights into the optimization of quantum resources while ensuring the accuracy of quantum state discrimination.
基金Project supported by the National Fundamental Research Program （Grant No 2001CB309310）, the National Natural Science Foundation of China （Grant Nos 90203018 and 10325523）, the Scientific Research Fund of Hunan Provincial Education Department of China （Grant No 04C385）, the Natural Science Foundation of Hunan Province of China （Grant No 05JJ30012） and the Science Foundation of Hunan Normal University of China.
文摘In this paper, we present a linear optical scheme for optimal unambiguous discrimination among nonorthogonal quantum states in terms of the multiple-rail and polarization representation of a single photon. In our scheme, discriminated quantum states are expressed by using the spatial degree of freedom of a single photon while the polarization degree of freedom of the single photon is used to act as an auxiliary qubit. The optical components used in our scheme are only passive linear optical elements such as polarizing beam splitters, wave plates, polarizers, single photon detectors, and single photon source.
基金supported by the Fundamental Research Funds for the Central Universities(Grant Nos.24CX03003A,23CX03011A,22CX03005A)the Natural Science Foundation of Shandong Province(Grant Nos.ZR2023MA025,ZR2021LL2002)from the NSFC(Grant Nos.11775306,11571220).
文摘In this paper,we study the problem of sampling complexity for channel discrimination with respect to two different strategies:product strategy and adaptive strategy.We first formally introduce the definitions of the sampling complexity of the channels under the framework of hypothesis testing,wherein the goal is to determine the minimum number of samples needed to reach a desired error probability.We then establish the lower and upper bounds on the sampling complexity of the symmetric,asymmetric,and error exponent hypothesis testing settings.We show that,by imposing product strategy on testing,the bounds are always characterized by the generalized channel divergence,while with adaptive strategy,the bounds are characterized by the amortized channel divergence.Finally,we analyze two concrete examples,and obtain that the adaptive strategy can not lead to an advantage to the problem of determining the sampling complexity for classical-quantum channels,which can bring advantages for generalized amplitude damping channels.
基金Project supported by the National Natural Science Foundation of China(Grant No.12201555)China Postdoctoral Science Foundation(Grant No.2021M702864)。
文摘We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems,the results presented here show that this property is no longer true in tripartite systems.Furthermore,we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination,that is,we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement.Lastly,we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence.It is interesting that the frozen phenomenon exists for geometric discord in this scenario.
基金Supported by the National Science Foundation of China under Grant Nos.11074002,61073048,and11104057the Natural Science Foundation of the Education Department of Anhui Province of China under Grant Nos.KJ2010ZD08,KJ2012A245the Doctor Research Start-Up Program of Huainan Normal University
文摘In this paper, we consider the minimax strategy to unambiguously discriminate two pure nonorthogonal quantum states without knowing a priori probability. By exploiting the positive-operator valued measure, we derive the upper bound of the minimax measurement of the optimal unambiguous state discrimination. Based on the linear optical devices, we propose an experimentally feasible scheme to implement a minimax measure of a general pair of two nonorthogonal quantum states.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11074002,61073048,and 11104057)the Natural Science Foundation of the Education Department of Anhui Province,China (Grant Nos. KJ2010ZD08 and KJ2012A245)the Postgraduate Program of Huainan Normal University of China
文摘Probabilistic quantum cloning（PQC） cannot copy a set of linearly dependent quantum states.In this paper,we show that if incorrect copies are allowed to be produced,linearly dependent quantum states may also be cloned by the PQC.By exploiting this kind of PQC to clone a special set of three linearly dependent quantum states,we derive the upper bound of the maximum confidence measure of a set.An explicit transformation of the maximum confidence measure is presented.
基金supported by the National Natural Science Foundation of China (Grant No. 10704001)the Natural Science Foundation of the Education Department of Anhui Province of China (Grant Nos. KJ2010ZD08 and KJ2010B204)the Doctor Research Start-Up Program of Huainan Normal University
文摘In this paper, we study the problem of multicopy quantum two-state discrimination. By exploring the quantum hypothesis testing, i.e., the probabilisfic quantum cloning, we derive the upper bounds of the minimal error discrimination （MED） and the optimal unambiguous discrimination （OUD）, which coincides with the Helstrom theorem and the JS limit. Furthermore, when prior probabilities are unknown, we derive the minimax MED and the minimax OUD. Based on the optimal NM probabilistic quantum cloning, we present the optimal strategies of collective measurements of the MED and the OUD. When the number of the copies is infinite, regardless of whether prior probabilities are known or not, the success probabilities of the MED and the OUD go to 100%, in accordance with the quantum measurement hypothesis that unknown quantum state can be determined if and only if infinite identical quantum state copies are given.
基金supported by the National Natural Science Foundation of China(Grant No.61632021)the Open Fund from the State Key Laboratory of High Performance Computing of China(HPCL)(Grant No.201401-01)
文摘Quantum computing is a significant computing capability which is superior to classical computing because of its superposition feature. Distinguishing several quantum states from quantum algorithm outputs is often a vital computational task. In most cases, the quantum states tend to be non-orthogonal due to superposition; quantum mechanics has proved that perfect outcomes could not be achieved by measurements, forcing repetitive measurement. Hence, it is important to determine the optimum measuring method which requires fewer repetitions and a lower error rate. However, extending current measurement approaches mainly aiming at quantum cryptography to multi-qubit situations for quantum computing confronts challenges, such as conducting global operations which has considerable costs in the experimental realm. Therefore, in this study, we have proposed an optimum subsystem method to avoid these difficulties. We have provided an analysis of the comparison between the reduced subsystem method and the global minimum error method for two-qubit problems; the conclusions have been verified experimentally. The results showed that the subsystem method could effectively discriminate non-orthogonal two-qubit states, such as separable states, entangled pure states, and mixed states; the cost of the experimental process had been significantly reduced, in most circumstances, with acceptable error rate. We believe the optimal subsystem method is the most valuable and promising approach for multi-qubit quantum computing applications.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11074002,61073048 and 11104057)the Natural Science Foundation of the Education Department of Anhui Province of China(Grant Nos. KJ2010ZD08 and KJ2012A245)the Postgraduate Program of Huainan Normal University
文摘We exploit optimal probabilistic cloning to rederive the JS limit.Dependent on the formulation given by the optimal probabilistic cloning,the explicit transformation of a measure of the JS limit is presented.Based on linear optical devices,we propose an experimentally feasible scheme to implement the JS limit measure of a general pair of two nonorthogonal quantum states.The success probability of the proposed scheme is unity.
