Some Notes On Wigner-Yanase-Dyson Skew Information And Coherence Of Quantum Operations

The Wigner-Yanase skew information was first proposed by Wigner and Yanase in 1963,it is an extension of the Fisher information in statistical theory,which has attracted wide attention of scholars of various countries in recent years.Quantum coherence is one of the most important properties of quantum me-chanics,and it is also the necessary condition of quantum correlation.It is the fun-damental characteristic of quantum mechanics,which is different from the classical mechanics.It is the key element of a series of physical phenomena,many quan-tum resource theories are based on it.Therefore,we should further study it's role in quantum information processing.In this paper,we discuss the Wigner-Yanase-Dyson skew information and quantum coherence by using the knowledge of operator algebra,operator theory and quantum mechanics.The Wigner-Yanase-Dyson skew information of different quantum channels are discussed;The concavity with the generalized Wigner-Yanase-Dyson skew information are proved;The coherence of the state in system HA are measured when a quantum operation acting on system HB,respectively.This article is divided into three chapters and arranged as follows:In Chapter 1,we introduce some symbolic representation and give some basic notations,concepts and theorems of the Wigner-Yanase-Dyson skew information and quantum coherence.Moreover,the research significance and current situation about our main contents are listed.In Chapter 2,we give some properties of the Wigner-Yanase-Dyson skew infor-mation and Wigner-Yanase correlation,on this foundation,we study the Wigner-Yanase-Dyson skew information of different quantum channels,prove the concavity of generalized Wigner-Yanase-Dyson skew information.In Chapter 3,we take a quantum operation on quantum system HB,and mea-sure the change of coherence after the operation.Firstly,we discuss that for a pure bipartite state,the coherence between two orthonormal rank 1 projections sum act-ing on HB and two orthonormal projections acting on HB,respectively.Secondly,the relation of coherence is obtained when random unitary channel ? acting on HB system.Finally,we get the the coherence of HA between the general quantum operation ?(?)=?nFn?Fn*acting on HB and the operation ?n(?)=Fn?Fn*on-HB.