Entropic Uncertainty Relation And Its Application In The Description Of Quantum Correlation And Quantum Phase Transition In Multipartite Systems

Entropic uncertainty relation is widely used in quantum information processing tasks,such as entanglement detection,quantum randomness and quantum key distribution,etc.In particular,the tripartite entropic uncertainty relation has an important application in the security analysis of quantum cryptographic protocols.Since the entropic uncertainty relation was proposed,it has been extended in various forms in order to obtain a more universal mathematical expression.Recently,the tripartite entropic uncertainty relation has been extended to multiple measurements setting.However,the lower bound of this proposed entropic uncertainty relation is not always tight for different measurements.Therefore,the optimization of the tripartite entropic uncertainty relation for multiple measurements needs to be further explored.In addition,it has been found that the upper bound of the shareability of quantum discord in a multipartite system can be obtained by using the tripartite entropic uncertainty relation.The quantum-memory-assisted entropic uncertainty relation is closely related to the competition between different quantum correlations in multipartite systems.On the other hand,quantum phase transition plays an important role in condensed matter physics,and the entropic uncertainty can be used to detect quantum phase transitions.In this paper,the entropic uncertainty relation and its application in the description of quantum correlation and quantum phase transition will be discussed further.The main contents of the thesis are divided into three parts.In Chapter 1,we introduce the basic concept and research progress of entropic uncertainty relation,and some typical methods of quantifying quantum correlations,and then introduce the relevant research of quantum phase transitions detected by uncertainty.In Chapter 2,we propose a new tripartite entropic uncertainty relation for multiple measurements,and prove analytically that the lower bound of this uncertainty relation is tighter than the previous one for measurements with mutually unbiased bases.We further study the relation between quantum memory assisted entropic uncertainty and different quantum correlations in multipartite systems.In Chapter 3,we study the quantum phase transitions identified by entropic uncertainty in the one-dimensional spin-1/2 Heisenberg spin chain.We show that the entropic uncertainty can be used as an effective tool to detect quantum phase transitions.At zero temperature,we consider the transverse field Ising model,XX model and XYT model with three-spin interaction,and use single-qubit uncertainty and two-qubit uncertainty to detect quantum phase transitions.In addition,we also study the quantum criticality phenomenon of entropic uncertainty at finite temperatures,and find that it can be used to estimate the temperature range of quantum criticality.In the last part of the paper,we summarize the main results and make an outlook for the study in the future.