Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This...Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This shows the existence of Quantum Zeno effect in the system with mixed initial states.展开更多
A sensor scheduling problem was considered for a class of hybrid systems named as the stochastic linear hybrid system （SLHS）. An algorithm was proposed to select one （or a group of） sensor at each time from a set ...A sensor scheduling problem was considered for a class of hybrid systems named as the stochastic linear hybrid system （SLHS）. An algorithm was proposed to select one （or a group of） sensor at each time from a set of sensors. Then, a hybrid estimation algorithm was designed to compute the estimates of the continuous and discrete states of the SLHS based on the observations from the selected sensors. As the sensor scheduling algorithm is designed such that the Bayesian decision risk is minimized, the true discrete state can be better identified. Moreover, the continuous state estimation performance of the proposed algorithm is better than that of hybrid estimation algorithms using only predetermined sensors. Finallyo the algorithms are validated through an illustrative target tracking example.展开更多
It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state. In other words, there does not exist a quantum cloning machine that can clone all qua...It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state. In other words, there does not exist a quantum cloning machine that can clone all quantum states. However, it is possible to clone given quantum states under certain conditions, for instance, k distinct pure states ｜ψ1〉, ｜ψ2）,....,｜ψk） can be cloned simultaneously if and only if they are orthogonal. This paper discusses the existence and construction of simultaneous cloning machines for mixed states. It is proved that k distinct mixed states Pl,P2 Pk of the n-dimensional quantum system Cn can be cloned simultaneously, that is, there exists a quantum channel Ф on .Mn ⊙ Mn and a state ∑ in Mn, such that Ф（ρi ⊙∑） = ρi ⊙ ρi for all i, if and only if ρiρj = 0 （i ≠j）. Also, the constructing procedure of the desired simultaneous cloning machine is given.展开更多
This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of...This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast scale.Such hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial stateobservation.This becomes in particular relevant when the dynamical systems are governed by partialdifferential equations.The authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such minimalregularity.As an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.展开更多
A phonon counting scheme based on the control of polaritons in an optomechanical system is proposed. This approach permits us to measure the number of phonons in a quantum non-demolition(QND) manner for arbitrary mode...A phonon counting scheme based on the control of polaritons in an optomechanical system is proposed. This approach permits us to measure the number of phonons in a quantum non-demolition(QND) manner for arbitrary modes not limited by the frequency matching condition as in usual photon-phonon scattering detections. The performance on phonon number transfer and quantum state transfer of the counter are analyzed and simulated numerically by taking into account all relevant sources of noise.展开更多
For symbolic reachability analysis of rectangular hybrid systems, the basic issue is finding a formal structure to represent and manipulate its infinite state spaces. Firstly, this structure must be closed to the reac...For symbolic reachability analysis of rectangular hybrid systems, the basic issue is finding a formal structure to represent and manipulate its infinite state spaces. Firstly, this structure must be closed to the reachability operation which means that reachable states from states expressed by this structure can be presented by it too. Secondly, the operation of finding reachable states with this structure should take as less computation as possible. To this end, a constraint system called rectangular zone is formalized, which is a conjunction of fixed amount of inequalities that compare fixed types of linear expressions with two variables to rational numbers. It is proved that the rectangular zone is closed to those reachability operations-intersection, elapsing of time and edge transition. Since the number of inequalities and the linear expression of each inequality is fixed in rectangular zones, so to obtain reachable rectangular zones, it just needs to change the rational numbers to which these linear expressions need to compare. To represent rectangular zones and unions of rectangular zones, a data structure called three dimensional constraint matrix(TDCM) and a BDD-like structure rectangular hybrid diagram(RHD) are introduced.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos. 10704001, 61073048, and 11005029the Key Project of Chinese Ministry of Education under Grant No. 210092+2 种基金the Key Program of the Education Department of Anhui Province under Grant Nos. KJ2008A28ZC, 2010SQRL153ZD, and KJ2010A287the "211" Project of Anhui University, the Personnel Department of Anhui ProvinceAnhui Key Laboratory of Information Materials and Devices Anhui University
文摘Quantum Zeno effect with mixed initial state is studied here. Frequent projective measurements performed on a bipartite joint pure state system will result in the quantum Zeno effect on the subsystem of interest. This shows the existence of Quantum Zeno effect in the system with mixed initial states.
基金Foundation item： Project（2012AA051603） supported by the National High Technology Research and Development Program 863 Plan of China
文摘A sensor scheduling problem was considered for a class of hybrid systems named as the stochastic linear hybrid system （SLHS）. An algorithm was proposed to select one （or a group of） sensor at each time from a set of sensors. Then, a hybrid estimation algorithm was designed to compute the estimates of the continuous and discrete states of the SLHS based on the observations from the selected sensors. As the sensor scheduling algorithm is designed such that the Bayesian decision risk is minimized, the true discrete state can be better identified. Moreover, the continuous state estimation performance of the proposed algorithm is better than that of hybrid estimation algorithms using only predetermined sensors. Finallyo the algorithms are validated through an illustrative target tracking example.
基金supported by the National Natural Science Foundation of China(Grant Nos.11401359,11371012,11171197 and 11301318)the Fundamental Research Funds for the Central Universities(Grant Nos.GK201402005 and GK201301007)+1 种基金the China Postdoctoral Science Foundation(Grant No.2014M552405)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2014JQ1010)
文摘It is a well-known fact that the no-cloning theorem forbids the creation of identical copies of an arbitrary unknown quantum state. In other words, there does not exist a quantum cloning machine that can clone all quantum states. However, it is possible to clone given quantum states under certain conditions, for instance, k distinct pure states ｜ψ1〉, ｜ψ2）,....,｜ψk） can be cloned simultaneously if and only if they are orthogonal. This paper discusses the existence and construction of simultaneous cloning machines for mixed states. It is proved that k distinct mixed states Pl,P2 Pk of the n-dimensional quantum system Cn can be cloned simultaneously, that is, there exists a quantum channel Ф on .Mn ⊙ Mn and a state ∑ in Mn, such that Ф（ρi ⊙∑） = ρi ⊙ ρi for all i, if and only if ρiρj = 0 （i ≠j）. Also, the constructing procedure of the desired simultaneous cloning machine is given.
基金support of the Elite Network of Bavaria under the grant #K-NW-2004-143
文摘This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast scale.Such hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial stateobservation.This becomes in particular relevant when the dynamical systems are governed by partialdifferential equations.The authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such minimalregularity.As an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.
基金supported by the National Key Research and Development Program of China(Grant No.2016YFA0302001)the National Natural Science Foundation of China(Grant Nos.11574086,91436211,11234003,and11654005)+1 种基金the Shanghai Rising-Star Program(Grant No.16QA1401600)the Science and Technology Commission of Shanghai Municipality(Grant No.16DZ2260200)
文摘A phonon counting scheme based on the control of polaritons in an optomechanical system is proposed. This approach permits us to measure the number of phonons in a quantum non-demolition(QND) manner for arbitrary modes not limited by the frequency matching condition as in usual photon-phonon scattering detections. The performance on phonon number transfer and quantum state transfer of the counter are analyzed and simulated numerically by taking into account all relevant sources of noise.
基金supported by the National Natural Science Foundation of China(Grant Nos.61373043&61003079)the Fundamental Research Funds for the Central Universities(Grant No.JB140316)
文摘For symbolic reachability analysis of rectangular hybrid systems, the basic issue is finding a formal structure to represent and manipulate its infinite state spaces. Firstly, this structure must be closed to the reachability operation which means that reachable states from states expressed by this structure can be presented by it too. Secondly, the operation of finding reachable states with this structure should take as less computation as possible. To this end, a constraint system called rectangular zone is formalized, which is a conjunction of fixed amount of inequalities that compare fixed types of linear expressions with two variables to rational numbers. It is proved that the rectangular zone is closed to those reachability operations-intersection, elapsing of time and edge transition. Since the number of inequalities and the linear expression of each inequality is fixed in rectangular zones, so to obtain reachable rectangular zones, it just needs to change the rational numbers to which these linear expressions need to compare. To represent rectangular zones and unions of rectangular zones, a data structure called three dimensional constraint matrix(TDCM) and a BDD-like structure rectangular hybrid diagram(RHD) are introduced.
