This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimat...This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimate is obtained.By averaging the fast components,we obtain an aggregated process.Although the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state space.Moreover,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.展开更多
Quantum key distribution provides an unconditional secure key sharing method in theory,but the imperfect factors of practical devices will bring security vulnerabilities.In this paper,we characterize the imperfections...Quantum key distribution provides an unconditional secure key sharing method in theory,but the imperfect factors of practical devices will bring security vulnerabilities.In this paper,we characterize the imperfections of the sender and analyze the possible attack strategies of Eve.Firstly,we present a quantized model for distinguishability of decoy states caused by intensity modulation.Besides,considering that Eve may control the preparation of states through hidden variables,we evaluate the security of preparation in practical quantum key distribution(QKD)scheme based on the weak-randomness model.Finally,we analyze the influence of the distinguishability of decoy state to secure key rate,for Eve may conduct the beam splitting attack and control the channel attenuation of different parts.Through the simulation,it can be seen that the secure key rate is sensitive to the distinguishability of decoy state and weak randomness,especially when Eve can control the channel attenuation.展开更多
We consider an open quantum system subjected to a noise channel under measurement-based feedback control and two prototypical classes of decoherence channels are considered： phase damping and generalized amplitude da...We consider an open quantum system subjected to a noise channel under measurement-based feedback control and two prototypical classes of decoherence channels are considered： phase damping and generalized amplitude damping. Based on quantum trajectory theory, we obtain an extended master equation for the dynamics of the reduced system in the presence of feedback control. For a qubit system we analytically solve this master equation and obtain the solution of the state vector dynamics. Then we propose an effective feedback control scheme for preparing an arbitrary quantum pure state. We also study how to protect two nonorthogonai states effectively, and find that projective measurement with unbiazed basis is not optimal for this task, while weak measurement with biased basis could realize the best protection of two nonorthogonal states. Furthermore, the inefficiencies in the feedback process are also discussed展开更多
Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. ...Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.Mathematics subject classification： 65N30, 90C46, 65N50, 49K20, 49N15, 65K10.展开更多
文摘This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimate is obtained.By averaging the fast components,we obtain an aggregated process.Although the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state space.Moreover,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.
基金the National Key Research and Development Program of China(Grant No.2020YFA0309702)NSAF(Grant No.U2130205)+3 种基金the National Natural Science Foundation of China(Grant Nos.62101597,61605248,and 61505261)the China Postdoctoral Science Foundation(Grant No.2021M691536)the Natural Science Foundation of Henan(Grant Nos.202300410534 and 202300410532)the Anhui Initiative in Quantum Information Technologies。
文摘Quantum key distribution provides an unconditional secure key sharing method in theory,but the imperfect factors of practical devices will bring security vulnerabilities.In this paper,we characterize the imperfections of the sender and analyze the possible attack strategies of Eve.Firstly,we present a quantized model for distinguishability of decoy states caused by intensity modulation.Besides,considering that Eve may control the preparation of states through hidden variables,we evaluate the security of preparation in practical quantum key distribution(QKD)scheme based on the weak-randomness model.Finally,we analyze the influence of the distinguishability of decoy state to secure key rate,for Eve may conduct the beam splitting attack and control the channel attenuation of different parts.Through the simulation,it can be seen that the secure key rate is sensitive to the distinguishability of decoy state and weak randomness,especially when Eve can control the channel attenuation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11274043 and 11375025
文摘We consider an open quantum system subjected to a noise channel under measurement-based feedback control and two prototypical classes of decoherence channels are considered： phase damping and generalized amplitude damping. Based on quantum trajectory theory, we obtain an extended master equation for the dynamics of the reduced system in the presence of feedback control. For a qubit system we analytically solve this master equation and obtain the solution of the state vector dynamics. Then we propose an effective feedback control scheme for preparing an arbitrary quantum pure state. We also study how to protect two nonorthogonai states effectively, and find that projective measurement with unbiazed basis is not optimal for this task, while weak measurement with biased basis could realize the best protection of two nonorthogonal states. Furthermore, the inefficiencies in the feedback process are also discussed
文摘Adaptive finite element methods for optimization problems for second order linear el- liptic partial differential equations subject to pointwise constraints on the l2-norm of the gradient of the state are considered. In a weak duality setting, i.e. without assuming a constraint qualification such as the existence of a Slater point, residual based a posteriori error estimators are derived. To overcome the lack in constraint qualification on the continuous level, the weak Fenchel dual is utilized. Several numerical tests illustrate the performance of the proposed error estimators.Mathematics subject classification： 65N30, 90C46, 65N50, 49K20, 49N15, 65K10.
