Theoretical Research On Quantum Detection And Application Of Super-conducting Quantum Circuit In The Frame Of Relativity

The theoretical research of quantum detection and the application of super-conducting quantum circuits are discussed under the framework of relativity in this thesis.Relativistic quantum information science is a new and popular interdisci-plinary subject in recent years.Its theoretical framework is rooted in relativity,quantum mechanics,quantum field theory,information science and so on.The main contents of this discipline include:the impact of relativistic motion and ef-fects on quantum systems,the impact of the structure and properties of curved space-time on quantum resources,and the exploration of how to explore space-time using cutting-edge techniques in quantum information.The development of relativistic quantum information is of far-reaching significance.Theoretically s-peaking,it is an important branch of quantum information theory.The combine of relativity theory and quantum information science has further expanded quan-tum information science and promoted the development of relativity theory and other theories of gravity.On the other hand,experimentally speaking,the re-search in this field provides creative methods and ideas for the detection of curved space-time.In this paper,the theoretical research of quantum detection is car-ried out in the context of non-inertial systems and curved space-time,using the theory of relativity as the framework and the method of open quantum system.Then,we further expand to the application field,based on the current supercon-ducting quantum circuit research,design superconducting quantum circuit and experimental scheme to simulate non-inertial soliton.The main conclusions come as follows:Firstly,we use the open quantum system method to discuss the quantum Fisher information?QFI?of phase parameters of a two-level atom with uniform circular motion coupled to an external field,and analyze how to improve the estimation accuracy of phase parameters of a two-level atom by adding boundary conditions.We find that:?i?The QFI of phase parameters decreased with time,and QFI decreased with the increase of centripetal acceleration without boundary;?ii?In the case of a boundary,QFI oscillates with the change of the distance between the detector and the boundary.When we select the appropriate position,QFI improves.?iii?When the atom is very close to the boundary,QFI tends to 1,which implies that the atom is shielded from the influence of the vacuum fluctuation by adding a boundary.Next,in order to detect the topological defects in the space-time of the cosmic string,we use a two-level atom which is coupled to a scalar field as a probe to estimate the loss-angle parameter,because the topological defects in this space-time are described by this parameter.In order to solve the quantum constraint of the estimability of this parameter,we study the QFI of the phase parameter.We obtain:?i?We obtain that QFI tends to the maximum value when the initial state of the detector is the excited state,which indicates that the excited state is the best initial state of the detector;?ii?We prove that there is an optimal evolutionary time for the detection process;?iii?We find that the optimal QFI decreases with the increase of acceleration,which indicates that the inertial detector is better than the uniformly accelerated detector in the estimation.Therefore,we provide a possible method to detect the space-time topology defects of cosmic strings.Then,we use a two-level atom as a detector to probe the space-time of the cosmic string to study how the geometric phase of the atom is affected by the topological characteristics of the cosmic string space,and compare it with the case in Minkowski space-time.Since it is very difficult to give a general analytic expression for the geometric phases in space and time in the universe,we discuss some specific examples to obtain the analytical results.We found that:?i?The case where the deficit angle parameter is equal to 1:our result is reduced to the result of Minkowski space-time;?ii?If the deficit angle parameter is greater than 1:first,we discuss the case where the atom is very close to the string,and compare the result with the case of minkowski spacetime.We find that the geometric phase is almost identical to the case where the atom is uniformly accel-erated in a Minkowski vacuum,except for one additional deficit angle parameter.Second,we find that when the defect angle parameter is 2,the geometric phase is similar to that of a uniformly accelerated atom with a reflective boundary in a Minkowski vacuum.Thus,our results show that the effect of nontrivial topology on the geometric phase of spacetime of cosmic strings is similar to the effect of reflection boundaries on the geometric phase of Minkowski spacetime.Finally,we discuss the application of superconducting quantum circuits.Due to the inhomogeneity of the medium and the noise generated by the coupling action,the solitons exhibit complex changing patterns.For solitons with vari-able mass,their motion is usually non-inertial,so it is difficult to directly study the behavior of solitons in the inhomogeneous medium in experiments.We are committed to using the superconducting quantum coherence circuit?SQUID?to simulate the behavior of the variable mass soliton,because we find that the circuit can be controlled by adjusting the external flux,thus achieving the purpose of simulating the behavior of the soliton.We have simulated following four kinds of the solitons:i)For the soliton with mass m=m₀?x²-t²?,the output figure shows that there is an intriguing flattening at the center.For short time interval limit,the above soliton shows the flattening prominently.ii)For the soliton with mass m=2m₀cos^?q?x±t?,it oscillates periodically in space-time.iii)For the soliton with mass m=m₀?2 cos q?x+t?cos q?x-t??^?/2,which at short time interval limit?t?0?gives m?x?????₀?cos qx?^?,and the soliton oscillates regularly.Similarly,for small space interval limit?x?0?,soliton oscillates regularly along time.And iv)for the soliton with mass m=m₀e^??x-x0?,the solitons first change with time and space,and then tend to stay the same.It is noted that the transmission line could effectively reduce the noise from the unwanted coupling and make the detection of the soliton more effectively,then the illustration about the realistic inhomogeneous systems will become more clear.