توصيفگر ها :
*C- جبر , جبر فون نويمان , اثر وفادار , نگاشت خطي مثبت , نگاشت خطي كاملا مثبت , كانال كوانتومي , متريك بيورس , وفاداري , نگاشت خطي مثبت تحويل ناپذير , دامنه ي ضربي , نگاشت شوارتز
چكيده انگليسي :
Bures contractive channels on operator algebras Azadeh Fakhri a fakhri@math iut ac ir January 20 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Seyed Mahmoud Manjegani manjgani@cc iut ac irAdvisor Dr Mehdi Nemati m nemati@cc iut ac ir2000 MSC Primary 46L05 Secondary 46L60 81R15 Keywords C algebra von Neumann algebra faithful trace positive linear map completely positive linear map quantum channel Bures metric fidelity irreducible positive linear map multiplicative domain Schwarz map Abstract This M Sc thesis is based on the following paper Douglas Farenick and Mizanur Rahaman Bures contractive channels on operator algebras New York Journal of Mathematics 23 2017 1369 1393 The concepts of the Bures metric and fidelity first was investigated by Donald Bures in 1969 in an effort to establish anotion of distance on the set of normal states of a von Neumann algebra 7 Later Uhlmann introduced the conceptof transition probability in the theory of quantum mechanics between two state of a algebra based on Bures s work which was later named as quantum fidelity of two states 60 Jozsa 38 and Alberti 2 applied these conceptsin the context quantum mechanics as a measure of closeness of quantum states Also several other authors includingNilsen and Chuang analysed the concept of fidelity to the distance between quantum states 48 Bengtsson and yczkowski 4 provided expository works on the Bures metric for density matrices and they showed that fidelity isa kind of transition probability Furthermore Hayashi 33 worked on the Bures metric for density metrices Afterthat there has been a lot of research on this topic It is considerable that the immense body of literature involvingfidelity only utilises the fact that fidelity is defined on normal states of von Neumann algebras When the von Neu mann algebra is bounded linear operators on a Hilbert space H that is B H all the normal states can be describedby the Trace functional Because of involving the definition of fidelity in the trace functional one can formulatethe notion of fidelity on arbitrary C algebras that possess faithful tracial states In general this thesis considers the study of quantum fidelity a distinguishability measure in the context of quantummechanics in operator algebraic point of view The notion of fidelity provides a quantitative measure of how closeone state of a quantum system is to another state High fidelity occurs when the two states are very close to eachother Obviously this concept and metric on the quantum states are closely related together which this metric onthe quantum states known as the Bures metric In this thesis fidelity and the Bures metric have been studied in thecontext of Unital C algebras that possess a faithful positive trace functional Finite von Neumann algebras that possess a faithful normal positive trace functional In details in unital C algebra A with a faithful trace functional the set D A of positive A such that 1 is an algebraic analogue of the space of density matrices The notion of density matrices is a set of allpositive matrices of a fixed dimension of unit trace There are several metrics of interest on spaces of density matrices Due to the relevant literature of the metric properties of the space of density matrices this thesis is motivated to study
