Research On The Observability Of Quantum Systems In Probability

In this paper, a new research on closed quantum system and open quantum system in finite dimensional space is proposed.Firstly,the indistinguishable states and the observability in probability are defined,then by means of Lie algebra and Lie group,the sufficient and necessary conditions to guarantee closed quantum system observable with a single measurement or multiple measurements are given and proved respectively.Besides,the whole state space is parted into observable subspace and unobservable subspace.Furthermore,as for open quantum system,according to Bloch geometrical representation,the sufficient and necessary conditions to guarantee open quantum system observable with a single measurement or multiple measurements are given and proved respectively.As well,the whole state space is parted into observable subspace and unobservable subspace. Lastly,the problem that how to determine the initial state are discussed,then algorithms are given.In addition, some analysis are delivered to illustrate the application.