Non-Markov Properties And Dense Coding In Open Two-body Spin Systems

quantum informatics is an interlaced subject developed together by quantum mechanics and information science,whose contents are numerous and complicated,among which quantum communication,quantum computation and quantum cryptography are currently the focus of attention.The most basic and important research in each of the above fields should be the study of quantum entanglement.In other words,without further exploration of quantum entanglement,there would have been no rapid development of quantum informatics.Therefore,more and more scientists are committed to the qualitative and quantitative research on the entanglement characteristics of condensed matter systems,and begin to propose a variety of entanglement schemes,and finally apply them to practice.For example,quantum dense coding,quantum teleportation,quantum cryptographic key distribution,quantum identity authentication and so on.In this paper,we mainly discuss the process and characteristics of quantum dense coding.It is well known that in the early stages of dense coding,researchers tend to ignore the interaction between the environment and the system for convenience,thus assuming that the quantum system is closed,but ignoring the entanglement dissipation or decoherence caused by environment noise is often too ideal.With the further development of dense coding process,in order to ensure the accuracy and universality of information coding,researchers pay more and more attention to the impact of environment noise on the system.For the above reasons,in this paper we also consider a non-markov environment.In fact,any quantum system will inevitably interact with the external environment.If there are correlations and entanglements between the initial states,the interaction between the system and the environment will lead to a long-term memory effect,then the markov approximation will fail,resulting in the non-markov properties of the system.Therefore,in this paper,the anisotropic Heisenberg XY chain is selected,and the function images of trace distance and entanglement measures with time are used to quantitatively analyze the mutual transformation between markov process and non-markov process.In addition,the Hamiltonian and density matrices are derived from diatomic systems under non-markov environments,and the properties of dense coded channel capacity are studied.The structure of this paper is organized as follows: in Section I,briefly introduces the emergence and development of quantum informatics and its research status and prospect,then lists the basic knowledge and theoretical support required by the second and third section of this paper,and finally explains the main research content and chapter arrangement of this paper.In Section II,we first introduce a composite model: the anisotropic Heisenberg XY chain.And then we write its Hamiltonian and density matrix.At last,two methods for measuring non-markov properties based on this model are studied,which are the measurement method based on trace distance and the measurement method based on quantum entanglement.Based on the above discussion,the advantages of the non-markov process are obtained: compared with the markov process,in the non-markov process,the subsystem and the auxiliary quantum system maintain a higher stable entanglement.In Section III,discussing the properties of quantum dense coding capacity in a diatomic system under the non-markov environment.The results show that: for different environment parameters ?(or ?),the initial value of dense coding capacity of channel ? is different,of which the greater the value of environment parameter ?(or ?),namely the more strongly the system is affected by the environment,the smaller the initial value of the dense coding capacity of channel ? is.For the same environment parameters ?(or ?),dense coding capacity of channel ? slowly decrease as time evolution finally tends to a stable value of the nonzero.This stability value depends on the initial state,not on the environment parameters,in other words,the environment noise only depends on the process of dense coding and does not determine the result.In addition,the entanglement purity r of the initial state also has a great effect on the the dense coding capacity of channel.At the same time,entanglement purity r has a positive effect on dense coding.When the entanglement purity r is constant,the value of the dense coding capacity of channel decreases slowly with the evolution of time and finally tends to a nonzero stable value.Therefore,in order to achieve an valid dense coding processing,the appropriate pure entangled state should be selected as far as possible.The section IV is the summary and discussion of the above research results.