Quantum Measurement Characterization And Simulation Based On Quantum Resource Theories

With the continuous progress of science and technology,the potential of quantum science has been gradually revealed.Some features of quantum mechanics have been found to improve the computation speed,increase the channel capacity and provide secure communication.In a complex quantum information processing system,in order to ensure the correct behavior of each device,it is necessary to characterize or certify them.As a basic module of all quantum information processing systems,quantum measurement is the only way for the observer to obtain information from the quantum system.The ability to obtain information directly restricts the effectiveness of information processing in a system.The properties of measurement reflect the ability of measurement.For example,non-projective measurement can perform better in state tomography.Therefore,it is necessary to characterize and classify the properties of measurement.For quantum state resources and quantum dynamic resources(including quantum measurement and quantum channel),quantum resource theory(QRT)provides a universal research framework.As the two properties of measurement,non-projectiveness and the number of outcomes have been reflected in the basic field of quantum information research and quantum applications.In this paper,we focus on these two intrinsic properties,and describe the measurement from the operator level and the quantum behavior level.Based on the QRT framework,we study the ability of the measurement of fixed number of outcomes and projective measurement to simulate other measurements.Finally,we study the application of multi result measurement in the production of random numbers.The main work of this paper is as follows:Firstly,in terms of operator based non-projectiveness,using the Choi form of channel,this paper successfully describes the set of projection measurement that can be obtained by classical transformation with semi-definite programming,which solves the open problem of predecessors.The results complete and enrich the non-proj ectiveness QRT and provide a tool for future research on non-projectiveness.Then,we use this characterization to calculate the maximum simulation success probability of the target measurement obtained by the post selection of the projection measurement,and then discuss whether the resource measurement generated by the post-selection has its advantages in quantum information processing.Secondly,in terms of the number of measurement outcomes based on operator,we describe the set simulated by measurements with fixed number of outcomes.These measurements with the same number of actual outcomes are regarded as free sets.Classical mixing and result remapping are free operations.Measurements with more than a given number of outcomes are resources.In this paper,the robustness of resources is given,and the relationship between the robustness of resources and the advantages of resources in state distinguishing tasks is established.The author also gives the maximum advantage of resources with multiple outcomes in state discrimination.In particular,the author points out that there are more extensive tasks that can be used to reflect the advantages of resources,and provide more possibilities for the application and development of resources.Thirdly,in terms of the number of measurement outcomes based on quantum behaviors,this paper proposes for the first time that in the preparation measurement experimental framework,based on the hypothesis of minimum overlap of the two prepared States,we can use semi-device-independent quantum behavior to describe the number of measurement outcomes.Given a lower bound of the overlap of states,this paper can verify whether a quantum behavior can be generated by the measurement of a certain number of outcomes by a semi-definite programming problem.Thanks to the simplicity of the two-input system,the author can parameterize the quantum measurement,and obtain an analytic section of the quantum behavior,so as to verify whether the number of outcomes is three or not.Finally,we find that the overlap of the states and the self-testing of the optimal measurement can be realized by using the quantum behavior generated by the unambiguous state discrimination(USD)protocol.Fourthly,in order to demonstrate the resource potential of multi-outcome measurement,a semi-device-independent random number generation protocol based on the lower bound of overlap of quantum states is proposed.The random number generated by this protocol is self detected by quantum behavior and is true random number under the premise of meeting the protocol assumption.Compared with the protocol based on USD selftesting,the protocol proposed in this paper can not only certify more random numbers,but also be more robust against noise.