Study On Related Issues In Quantum Measurement

In classical physics,the position and momentum of a particle can be determined simultaneously,but in quantum mechanics they cannot be determined simultaneously.With the development of quantum mechanics and quantum measurement theory,the effect of simultaneous measurement of non-commuting variables on the Heisenberg uncertainty relation has become a problem of interest to researchers.Quantum measurement theory not only provides a new theoretical method for the study of Heisenberg’s uncertainty relation,but also helps people understand Heisenberg’s uncertainty relation.At the same time,quantum measurement theory has promoted the rapid development of quantum mechanics,quantum information and quantum thermodynamics.The Landauer’s principle states the lowest energy limit for erasing or gaining infor-mation in a measurement.Landauer’s principle establishes a connection between ther-modynamics and information theory.Landauer’s principle saves the second law of ther-modynamics from the paradox of Maxwell’s demon.In recent years,the effectiveness of Landauer’s principle in quantum thermodynamics has attracted widespread attention from researchers.This paper mainly studies the effect of simultaneous weak measuremen-t of non-commuting variables on the Heisenberg uncertainty relation and the validity of Landauer’s principle under strong coupling between system and environment.The specific research is as follows:1.Research on the influence of simultaneous weak measurement of non-commuting variables on the Heisenberg uncertainty relation:（1）Proposing a simultaneous weak mea-surement scheme for non-commuting variables;（2）shows how to obtain the weak values of the corresponding variables,and get the relationship between error and disturbance accordingly;（3）The coupling strength between pointer and system and the observable measurement and state of quantum bit are changed to observe the error of weak measure-ment of two noncommutative variables at the same time.2.Research on the validity of Landauer’s principle under the strong coupling of system and environment:（1）The definition of work and heat under strong coupling between the system and the environment is given by using the method of quantum mechanics;（2）shows the Landauer principle under the strong coupling of system and environment;（3）It is shown that strong coupling of the system to the environment removes the lower bound on the work expended in the combined process of measuring and erasing,confirming the results regarding the violation of Landauer’s principle;（4）Based on the⁴⁰Ca⁺ion trap,an experimental scheme was proposed to verify the result of the violation of Landauer’s principle under the strong coupling between the system and the environment.3.The results show that:By properly choosing the observables and states of the qubit,the error of the simultaneous weak measurement of two invariant variables outperforms the Heisenberg uncertainty relation exhibited by the error and the perturbation,Based on this result,it is proved that once the coupling strength is non-zero,there will always be a transcendence phenomenon;Strong system-environment coupling is the main factor of Landauer’s principle,and the violation of Landauer’s principle occurs in the Rabi frequency range,and the increase of attenuation rate contributes to the violation of Landauer’s principle;A violation of Landauer’s principle occurs when the coherence j is greater than a threshold,and will then increase with increasing coherence C_l1;In the case of lower temperature,the violation of Landauer’s principle is more obvious.