Theory Research Of Weak Value And Weak Measurement In Quantum Measurements

Quantum mechanics is the foundation of modern physical theories and quantum measurement is the virtual part in the development of quantum mechanics. As the important part of quantum information, quantum measurement can not only be applied to the investigation of physical word, but also the be powerful tool in the military, precise instrument, commercial manufacture and so on. New methods and experimental structures appeared in quantum measurement are widely used in many areas. Weak value and weak measurement, as the spotlight in quantum measurement and indirect measurement, is gradually cause the attentions of scientists. Its potential in unknown parameter estimation is in the urgent need of kinds of research.The system of weak measurement is unlike the direct projection in traditional quantum measurement, where the postselection of ancilla state results in the amplifi-cation in system state. In the ”weak” coupling of ancilla and system states, the weak measurement can be effective approximated in linear regime. Weak value is far away the range of eigenvalues, and at the same time as a complex value weak measurement shows advantages in a lot of aspects. Weak measurement can extract a lot of information in the low detected possibility, which can make up of the shorts of detectors.The un-classical properties of weak measurement and weak value provides the theories quantities of quantum paradox. Weak value and weak measurement can further the understanding of weak measurement.To prompt the research of weak measurement and weak value, the thesis are focused in the following:1.We brie?y describe the quantum measurement theory. we introduce the coherent state and its properties, the differences between entangled and separable states. The definition of projective measurement and POVM measurement is detailed and is helpful in the understanding of weak measurement. The correlation function and its use in parameter estimation is introduced.2.The definition and experimental realization of weak value and weak measurement is shown. The Hermitian operator and unitary operator corresponding to weak interaction parameter have different structures. The weak measurement needs the two freedom space we called system state and ancilla state. The photon number propertied of coherent state in weak measurement and amplification in it is further discussed.3.Entanled state in ancilla state can improved the resolution of parameter estimation. The use of weak measurement and entangled ancilla can effectively approach the Heisenberg limit.4.Derived from the HBT experiment, under the development of many years, quantum correlation function has been widely used in ghost imaging, precision measurement, clock synchronization and so on. We investigate the combination between weak measurement and multi-order correlation function and get the high resolution in parameter estimation. The result shows that the real weak value in entangled state situation has the advantages compared with imaginary one. The separable shows no advantages since the rapid decrease in detection probability.The thesis concerns the weak measurement in quantum measurement and quantum metrology, which can enhance the applications in parameter estimation and quantum precision measurement.