Some Research Of Quantum Coherence

Quantum coherence is an important physical resource.Because it is an important premise for realizing quantum communication and quantum information,it is widely used in modern information processing tasks as people accumulate experience in microcosm.In recent years,quantum coherence resource theory has become an important research topic in quantum mechanics,quantum optics and quantum information.This direction has attracted the extensive attention of quantum information experts at home and abroad.There have been achievements in the characterization of pure state and mixed state in quantum theory,but the concept,properties and characterization of coherence are not perfect,which is also the main problem of this paper.This article is divided into four chapters,the specific content is as follows:The first chapter first gives some of the symbols used in this paper,and some basic concepts,hypotheses and theorems of quantum coherence,and their development process,research significance and current situation are introduced.In the second chapter,we first give the necessary and sufficient conditions for a bounded linear operator to be an incoherent operator,the Concrete expression of the incoherent operator,and the conclusion of characterizing the incoherent quantum operation with the incoherent operator.Then we give the concrete form of the strongly incoherent operator,and obtain two equivalent definitions of the strictly incoherent quantum operation.In addition,we get the conclusion that the strictly incoherent quantum operation is the true subset of incoherent quantum operation.We also verify our conclusion with examples,and we can judge whether an operator is incoherent or strongly incoherent more easily.Specifically,we can judge whether an operator is an incoherent or strongly incoherent operator from its form directly,and then get whether its corresponding quantum operation is incoherent quantum operation or strictly incoherent quantum operation.This provides a convenient method for the research of incoherent quantum operation and strictly incoherent quantum operation.The third chapter introduces an example of dephasing-covariant quantum operation and an example of quantum operation that is not dephasing-covariant.Then we give the necessary and sufficient condition that the kraus operators of quantum operation are e-incoherent operator,and discuss the properties of the corresponding quantum operation.We also give the relationship between the dephasing-covariant quantum operation and the strictly incoherent quantum operation.The relationship between the strictly incoherent quantum operation and the fully incoherent quantum operation is also given.We also get the coherence of the quantum state becomes smaller after the effect of the dephasing-covariant quantum operation when H is taken as C2.The relationship between the incoherent quantum operation and the dephasing-covariant quantum operation is also given.The necessary and sufficient conditions for the symmetry of the pure state under the observable measurement are given.The relationship between the incoherent quantum operation and the translationly invariant is also given.The sufficient condition for quantum operation is translationly invariant quantum operation is given,and the relations between bit reversal channel?phase reversal channel.depolarization channel and translationly invariant quantum operation are also given.The fourth chapter introduces some characterizations of the coherence of two quantum computer models acting on mixed states.