Research On Quantum State Protection And System Characterization Via Quantum Control

Quantum technologies have an important impact on modern cryptography.On the one hand,quantum computing seriously threatens the security of modern cryptography;On the other hand,quantum cryptography provides a candidate to resist the attack of quantum com-puting.Coherence is one of the basic principles that quantum technologies show advan-tages over their classical counterparts.However,it is vulnerable to the environment and thus causes decoherence.Before suppressing decoherence,there is an important task,i.e.,describing the initial state,the dynamic,and the noise of an unknown system with an ap-propriate mathematical model.This is also called quantum system characterization.With the increasing demand for practical quantum technologies,eliminating or reducing the effect of decoherence and characterizing an unknown quantum subsystem have become important tasks in quantum information processing.In this dissertation,we study two main problems:state protection and system character-ization in the existence of decoherence.Based on the correlation between quantum control and decoherence,we design control schemes to preserve coherence and propose a control method to characterize an unknown quantum system.The details are as follows:Firstly,we studied the protection of two nonorthogonal qubit states with equal a prior probability against amplitude damping noise.We found that there was a dilemma between"high fidelity" and "high success probability" in existing quantum feedback control(QFBC)and quantum feedforward control(QFFC)for such a protection task.To solve this problem,we present a quantum composite control(QCC)scheme to achieve relatively high fidelity and success probability.In this scheme,the postweak measurement in QFFC was treated as a measurement in QFBC.Compared with previous schemes,when success probability was fixed,QCC scheme achieved the highest fidelity;when fidelity was fixed,QCC scheme completed protection with the highest success probability.Furthermore,our scheme can be experimentally implemented with current technologies.Secondly,we studied the protection of two nonorthogonal qubit states with arbitrary prior probabilities against amplitude damping noise.There were two motivations.On the one hand,previous control schemes achieved relatively low fidelity when the nonzero initial phase was considered.On the other hand,existing quantum control schemes only considered state protection with equal prior probability,while states with arbitrary prior probabilities were more general.Based on these,we present a prior-information induced quantum com-posite control scheme,where parameters were introduced in measurements and corrections to balance the effect of prior information(i.e.,prior probabilities and initial states).The fi-delity in our scheme achieved no less than 0.933 for any parameters θ,Φand s in states and the parameter r in noise when the success probability was required to be unit.Besides,when compared to previous control schemes,the success probability had an exponential improve-ment for some states when the fidelity was fixed.Thirdly,we studied the problem of bipartite quantum system characterization.Existing techniques need either specific Hamiltonian assumptions or unlimited allowance to the quan-tum system.Practical consideration arose when only limited access was allowed in quantum materials or platforms,such as nitrogen-vacancy-centers.Based on this,we analyzed such a problem with a general stationary Gaussian noise assumption via limited access to the sys-tem.By choosing appropriate fast controls on subsystem 1 and slow control on subsystem 2,one can derive the initial state and effective noise spectrums on the total system from the measurement results of subsystem 1.