Quantum State Discrimination And Its Application In Parameter Estimation

As an experimental science,the entire theoretical framework of physics needs to be tested by experimental data,so measurement has become one of the most basic concepts of physics.Quantum information,one of the branches of physics that has flourished in recent decades,combines quantum mechanics and information theory to encode information with quantum states as a vehicle for computing speed,security,or measurement accuracy beyond classical.In order to obtain information encoded in quantum states,quantum measurements have become an unavoidable topic.Quantum measurements are often expressed as operators with many properties that differ from classical measurements,such as the effects that measurements have on quantum states.Essentially,a measurement consists of multiple projection operators,each of which projects a quantum state into a subspace,and the meaning of the measurement is to identify which subspace the quantum state belongs to.The difference between the classical world and the quantum world is that quantum states can be nonorthogonal,so the measurement can not perfectly identify the quantum state.We can only construct appropriate measurements to distinguish different quantum states as much as possible,this problem is called quantum state discrimination.In the field of quantum information,it is often necessary to take the quantum states as the carrier of physical parameters.The quantum state is transformed according to the physical parameters,and then we need to discriminate the quantum states to extract the information of physical parameters.Therefore,the quantum state discrimination is often inseparable from the parameter estimation.The successful discrimination of the quantum state is the premise of the parameter estimation.In this paper,we mainly study the problems related to the discrimination of quantum states and their application in parameter estimation,and discuss the experimental implementation scheme of related strategies,laying a foundation for their application and promotion.The main research results are as follows:1.We give the optimal discrimination strategy for the binary pure state discrimination scenario under the multi-person information distribution scenario.The mutual information is extended and a special set of sequential weak measurements is constructed.It is proved theoretically that all mutual information can be extracted by using this sequential weak measurement without information being destroyed or left behind.Finally,we use the high-quality entangled source and the cascaded Mach Zehnder interferometer as the hearalded single photon source and weak measurement experimental devices respectively.In the experiment,we study the actual effect of this strategy in the linear optical platform.2.Through simulation calculation,it is found that the constructed sequential weak measurement is not sensitive to quantum states,that means it will not excessively affect its ability to extract information because of the change of quantum states,and by changing the intensity parameters of the measurement,it is convenient to adjust the amount of mutual information that each person can obtain without destroying information.The above features will contribute to the promotion of this strategy in practical application scenarios.3.Combine the concept of quantum self-testing with quantum state discrimination strategy to achieve a trusted quantum remote sensing scheme.The traditional remote sensing scheme requires the remote site personnel to transmit the measured data to the local server to assist in judgment,but the data to be transmitted by the remote server may be eavesdropped and tampered with.We introduce quantum nonlocality into the remote sensing scheme,encode the information of the parameters to be measured in some entangled states through the quantum entangled states conversion process,and then use the quantum states self-testing to detect the specific form of the converted quantum states,so as to estimate the parameters to be measured.Because the local operation cannot forge quantum nonlocality,the scheme,which is partial device-independent,can resist the eavesdropper’s attack on the remote server and obtain reliable remote sensing results.We also applied the scheme to the scene of mineral resources exploration,and studied the optical experimental device to realize the scheme.