Research On Entropy Uncertainty Relationship And Quantum Entanglement In The Bipartite System

With the development of science and technology,the mystery of the quantum field has gradually been unveiled by many scientists.The uncertainty principle is one of the important contents of quantum theory and is considered to be an important property different from classical physics.Because entropy has abundant applications in quantum information processing,some researchers consider introducing the concept of entropy into the uncertainty principle.Regarding the development of the entropy uncertainty relationship,the biggest contribution is that Berta et al.not only extended the entropy uncertainty relationship of a single-qubit system to the case of a two-qubit system,but also extended it to more complex systems.This provides a solid foundation for applications in quantum communications,quantum computing and other fields to realize the combination of theory and practice in the quantum field.At the same time,it provides the feasibility for the study of the entropy uncertainty relationship under multi-measurement in high-dimensional systems.The relationship between the entropy uncertainty relationship and the two basic physical concepts of quantum entanglement is more complicated.For example,for a Bell-like state,as the quantum entanglement increases,the entropy uncertainty shows a decreasing trend.Of course,this is the result of discussion under ideal circumstances,but quantum systems inevitably interact with the environment in which they are located.This requires consideration of the impact of interaction on the system.Moreover,we can use the entropy uncertainty relationship to detect the quantum entanglement of the system,that is to say,the entropy uncertainty relationship can be used as an important criterion for quantum entanglement.For quantum entanglement,intrinsic concurrence is proposed to extend the complementarity in the pure state to the mixed state.This article mainly studies the dynamic behavior of the entropy uncertain relationship in the open system,the relationship between the two quantities of concurrence and intrinsic concurrence.Our main jobs are as follows:(1)For the three-measurement entropy uncertainty relationship,we let the quantum system interact with the non-Markovian and Markovian channels respectively.The dynamic characteristics of the entropy uncertainty obviously reflect the characteristics of the related two types of channels,that is,whether the entropy uncertainty shows the phenomenon that the oscillation decays to the saturation value.What's interesting is that the entropy uncertainty and quantum detuning show an incomplete anti-correlation phenomenon.Through derivation,it can be found that the uncertainty entropy not only depends on the associated evolution of the quantum system composed of A and B,but also depends on the conditional entropy of the subsystem.Then,by constructing another set of measurement basis and comparing it with the frequently used Pauli measurement,it is found that for different quantum initial states,the selected measurement basis has different effects on the entropy uncertainty.As for the number of measurements,adding one more measurement result will also increase the entropy uncertainty,indicating that the measurement will lead to an increase in uncertainty.In addition,some quantum operations can be combined to suppress the influence of the external environment on the quantum system.For this reason,we provide a simple and effective method,and can obtain the optimal operation intensity for the best effect of environmental suppression.Finally,we use the basis of judging whether there is entanglement in the quantum system to study the dynamic behavior of the entropy uncertainty of the three measurements.(2)Concurrence is one of the most common measures of quantum entanglement.Recently,someone proposed a new concept derived from symbiotic entanglement—intrinsic concurrence.From the description of the concept,it can be seen that there must be a special relationship between concurrence and intrinsic concurrence.We first analyze the relationship between concurrence and intrinsic concurrence of the maximally nonlocal mixed state,and draw an inequality relationship between the two quantities of concurrence and intrinsic concurrence.Then we verify this inequality by selecting the random state of the two-qubit system and some typical quantum states,and the result verifies the validity of the inequality very well.This will help us to better study the related properties of quantum entanglement.