Research On Related Problems Of Open Quantum System Dynamical Process

In this thesis,we apply functional analysis and operator theory to study quantum Markovianity,decoherence-free subspaces,generalized duality quantum coputers which are closely related to open quantum system dynamical processes.Master equation and quantum operation are usual approaches for the description of open quantum system dynamical processes.Based on the divisibility definition of quantum Markovianity,the Mokovianity of tensor product,pointwise product and convex combination of two Markovian quantum dynamical processes is discussed and a new witness of quantum non-Markovianity is proposed.After an investigation of the existing decoherence-free subspace definition,four new kinds of decoherence-free subspaces are defined and characterized,and the relations a-mong different kinds of decoherence-free subspaces are explored.We also develop a generalized duality quantum computer acting on mixed states,which is essentially a generalized quantum operation,and analyze its structure and basic properties.There are four chapters in this thesis.The main contents of each chapter are as follows.In the first chapter we give an introduction to the background,the recent developments,and the related prior knowledge.In the second chapter,the operational closure of Markovian quantum dynami-cal processes and the witness of non-Markovian quantum quantum dynamical pro-cesses are investigated.Firstly,we construct a quantum dynamical process which seems like a staircase funtion and give the necessary and sufficient condition for the quantum dynamical process to be Markovian,after a discussion of the divisibility definition of Markovian quantum dynamical processes.Secondly,the Mokovianity of tensor product,point-wise multiplication and convex combination of two Marko-vian quantum dynamical processes is studied respectively and some basic results are attained:it is proved that the tensor product of two Markovian quantum dynamical processes is still Markovian,a sufficient condition for the pointwise product of two Markovian quantum dynamical processes to be Markovian is suggested,two exam-ples are constructed to respectively illustrate that the sets of one-qubit Markovian and one-qubit non-Markovian quantum dynamical processes are not convex.Final-ly,we develop a new witness of non-Markovian quantum dynamical processes by exploiting the correlation flow between the system and its environment,and present a specific application example.In the third chapter,the definitions of decoherenc-free subspaces of open quan-tum system Makovian dynamical processes are analyzed and characterized under the setting of the system space being a finite-dimensional Hilbert space,and the relations among several different kinds of decoherence-free subspaces are explored.Firstly,after reviewing the definition and characterization of general decoherence-free subspace(GDFS),we propose and characterize a new kind of time dependant decoherence-free subspaces,i.e.the ideal decoherence-free subspaces,and furtherly show the connections among the existing three kinds of decoherence-free subspaces and the newly-defined kind of decoherence-free subspaces.Secondly,the time in-dependant restricted decoherence-free subspace,general decoherence-free subspace and ideal decoherence-free subspace are generalized to time dependant case.we make characterizations of the three new kinds of decoherence-free subspaces respec-tively,and obtain the relations among four kinds of time dependant decoherence-free subspaces,where the fourth kind is the existing so-called time dependant extended decoherence-free subspaces.In the final chapter,we propose the generalized duality quantum computer act-ing on mixed states(GDQC-MS),and investigate its structure and basic properties.By adapting two components of the generalized duality quantum computer acting on vector states(GDQC),i.e.the quantum wave divider and the quantum wave combinator,the GDQC is generalized to a GDQC-MS.We study the properties of the new duality quantum computer and its components,prove that the dividor and the combiner of the computer are mutually dual and both of them are contractions.When the GQOs in a GDQC-MS are all contractions,we discover that the corre-sponding operator UL? of a GDQC-MS is also a contraction,and the loss of an input state passing through a GDQC-MS is measured in this case.It is also proved that UL? is a general quantum operation(GQO).And the dual operator of UL? is proved to be a GQO under the conditions that ?k(I)? I(k=1,2,…,n).