Local Discrimination And Schmidt Decomposition Of Multipartite Quantum States In Quantum Information Theory

In this dissertation, some problems related to two fundamental issues in quantumcomputation and quantum information theory, namely, local quantum state discrimi-nation and existence of Schmidt decomposition for an arbitrary multipartite quantumpure state, are discussed. After a brief review of quantum information theory, the au-thor presents in detail some results related to these two problems, obtained during hisstudy toward a Master degree. To be more specific,1. By constructing an explicit and simple local discrimination protocol, the authorshows that two copies are enough to discriminate a complete basis set of maxi-mally entangled states in canonical form.2. The author considers the problem of existence of Schmidt decomposition for anarbitrary multipartite quantum pure state and derives a necessary and sufficientcondition for the existence of Schmidt decompositions for a given multipartitequbit pure state. Existent results about simultaneous Schmidt decomposition forbipartite states are also generalized and a necessary and sufficient condition isalso worked out for the special case of real coefficients for tripartite qubit states.3. The author discusses the connection between simultaneous Schmidt decomposi-tion and local discrimination of multipartite quantum pure states and proves thatglobal optimality of discrimination efficiency can be reached under LOCC(LocalOperations and Classical Communication) by constructing an explicit protocol.