Certain Researches On Quantum State Discrimination And Quantum Key Distribution

Quantum information theory is one of the most-researched areas in recent years,whose aim is applying quantum theory in communication.This dissertation mainly contains two research areas,one is quantum state discrimination and the other is quantum key distribution.The discrimination of quantum states is one of the key problems in quantum information theory.No matter what tasks are going to be implemented,estimating channels and devices should come into the first place.The only way for such estimates is inputting certain states,which are usually under controlled and measuring the corresponding output states,which depend on the channel.Therefore,the problem is discriminating unknown states.Naturally,it has substantial applications in researches such as state preparing,checking,noise estimating and secure communication.For quantum state discrimination,this dissertation mainly investigates state tomography,whose aim is determining an unknown state by inputting a series of coherent states and measuring the corresponding outputs,as well as distinguishability,which focuses on whether states can be distinguished via a series of manipulations such as local operations and classical communications(LOCC).The main results include:(1)We present certain conditions of informationally completed(IC)measurements,demonstrating the difficulty of constructing minimal projective informationally completed measurements(MPICM).However,we propose several examples of MPICM,as well as a general construction for even-dimensional systems,conjecturing its validity with numerical proof for systems whose dimensions are not more than 100.We also research two kinds of optimality of IC measurements including in the senses of observable efficiency and frame potential,and tomography via a single projective measurement as well as local measurements;(2)We prove that certain distinguishabilities of states are independent with the dimension of quantum system,demonstrating that they are properties of states themselves.As corollaries,a LOCC indistinguishable orthogonal product basis can be constructed while the minimum number of LOCC indistinguishable orthogonal product states can be given,in a general system;(3)We prove for a bipartite system that N orthogonal product states can be distinguished by LOCC via[N/4]copies while for a multipartite system that N orthogonal product states can be distinguished by LOCC via[N/4]+1 copies,giving upper bounds of copy consumption for distinguishing orthogonal product states by LOCC.Quantum key distribution is one of the most significant applications in quantum information theory,whose aim is obtaining secure communication by quantum theory.The most-used cryptosystem nowadays,namely RSA system,is not secure in quantum era.The only cryptosystem proven to be secure is coding with an one-time pad,which however,could not be transmitted securely via classical communications.But on the other hand,theoretically,it is possible to transmit an one-time pad via quantum methods securely,which is called quantum key distribution(QKD).For QKD,protocols,noises,security,efficiency and practical devices should be considered.The investigations in this dissertation contain QKD protocols,noise processings,generalized protocol and calculations of secure bound,measurement-device-independenization,as well as single photon detector(SPD)problems.The main results include:(1)As basic introduction,we present several QKD protocols with abecedarian analysis and comparation with certain previous protocols;(2)We present a scheme,dealing with noises,with which QKD protocols could be implemented via noisy channels without errors;(3)We provide an abstraction of prepare-measure QKD protocols and investigate two special cases,which are optimal among all protocols coding by the same states.We calculate their secure bound of qubit error rate(QBER)under special attacks;(4)We investigate measurement-device-independent quantum key distribution(MDI-QKD),providing a scheme without employing joint measurements.More significantly,our scheme could be applied to general prepare-measure QKD protocols,making them become MDI-QKD protocols.For implementing practically,we investigate the photon-number-adding(PNA)attacks and provide a solution;(5)We investigate the SPD problem,providing a scheme,with which today’s SPD can be employed as perfect ones.In particular,it solves the dark count problem and removes the restriction of QKD distance caused by SPD.