Clone, Delete, And Distinguish Between The Probabilistic Teleportation Of Quantum Information

The quantum information have the character of the non-locality by comparison of the classical information,some quantum states have the character:entanglement. and we all know that the classical information does not have this character.With the help of entanglement of quantum state,some tasks,which could not be realized in classical information theory,but could be realized in quantum information completely.In this dissertation,some problems related to fundamental problems in quantum computation and quantum information theory are discussed.1 In the chapter 3,using the reduced density operator of quantum state,we study the delete and clone of quantum information.Testify that there exists no quantum delete machine which makes the deleted states and the blank states to be correlated;we can not construct a machine to perfectly delete arbitrary mixed quantum states.We consider the problem of cloning and deleting of mixed quantum states in the case of probabilistic form,obtain a necessary condition in the form of probability with a unification formula.By using the results obtained,the processing of quantum information can be further comprehended and have aspiring significance quantum computer.Indeed we construct a type of a machine which approximately deletes a copy such that the fidelity of deletion does not depend on the input state. And the fidelity of the machine is slightly greater than the fidelity of some machine.Although under the condition of global operation,the non orthogonal quantum states cannot be copied and deleted perfectly because of the linearity of the quantum operation,the orthogonal states could be copied and deleted perfectly.But when the operation is restricted to the local operation and classical communication(LOCC). ever the orthogonal quantum states may be not being copied and deleted perfectly, we consider the problem of deleting of bipartite orthogonal maximal entanglement states and deleting of quantum channel,also derive some necessary conditions when they could be deleted(LOCC).2 The discrimination of quantum states is the one of basic problems in quantum information.It is well known that the no locality without entanglement is an interesting research field.The orthogonal states could not been distinguished if the quantum states are be shared by multiparty(specials discretely),then they could not be perfectly distinguished globally but be distinguished by local operations and classical communication (LOCC).The discrimination of pure states by LOCC is studied by the most literatures,but not the mixed states.So it is importation to take into account the discrimination of mixed states.Second,we consider the perfectly discrimination of mixed quantum,and using the Schmidt number of the states to consider the problem. obtain two necessary conditions.One is that.discrimination of mixed states by LOCC.the quantum states should be product states:on the base of the results. we also prove that two arbitrary bipartite orthogonal produced states can be distinguished by LOCC.The other one is that the sum of the Schmidt numbers of the mixed states should less than the dimension of the Hilbert space which the states belong to.Then we turn to study the localy distinguish of n(?)n quantum system,and we consider the distinguish of the sets of which contain some GHZ-states.With POVM measurement transformation,we consider geometrically uniform (GU) states sets and the copound GU(CGU) states sets,we derive two lower bounds for the average failure probability of unambiguous discrimination of symmetric mixed quantum states.Then we consider the perfect discrimination problem which apply the method of unambiguous discrimination quantum states to quantum operation,and get a necessary and sufficient condition for quantum operation;second we extend set discrimination of quantum states to set discrimination of quantum operation,at the same time obtain two necessary and sufficient conditions for quantum operation.3 The quantum entanglement is the necessary resource,which could realize some quantum tasks.In chapter 5,we describe a protocol for multi-qubit quantum teleportation between two parties with control of many agents in the networks.Our method seems to be different from the method proposed recently.The quantum channels we used is not maximally entangled state.So we show that the senders can only probabilistic restore the qubit even if all the agents cooperate with the receiver and the protocol suit to the realityIt is very important to study the algorithm for the entanglement transformation between the quantum states determinately or probability.An algorithm first is presented that transforms one bipartite quantum state into a mixed bipartite by local operations and classical communication,which is much simpler than the original algorithm.The other algorithm for the transformation between two bipartite states with catalysis by LOCC is also discussed.Entropy is a measurement of information which describes the uncertainty of a information system or quantifies how much information we gain on average.Using a mathematical characterization of a function and the Tensor product of matrix,we discuss the inequalities on the Tsallis relative operator entropy,the upper and lower bounds of the Tsallis relative operator entropy are derived.The researching results from the thesis consist of the followings statements.(1) Testify that there exists no quantum delete machine.Meanwhile,a necessary condition in the form of probability with a unification formula is given,we construct a type of machine which approximately delete a qubit.We consider the problem of deleting of bipartite orthogonal maximal entanglement states and deleting of quantum channel,also derive some necessary conditions when they could be deleted.(2) We consider the discrimination of mixed quantum,and using the Schmidt number of the states to consider the problem,obtain some necessary conditions. meanwhile,consider the distinguish of the sets of which contain some GHZ-states. Discrimination of geometrically uniform states sets and the copound states sets be studied,derive two lower bounds for the average failure probability of unambiguous discrimination of symmetric mixed quantum states.Unambiguous discrimination of quantum operation is considered,get a necessary and sufficient condition for quantum operation:second we extend set discrimination of quantum states to set discrimination of quantum operation,at the same time obtain two necessary and sufficient conditions.We study the mathematical characterization of the entanglement transformation.(3) Describe a protocol for multi-qubit quantum teleportation between two parties with control of many agents in the networks.An algorithm is presented that transforms one bipartite quantum state into a mixed bipartite by local operations and classical communication.Discussing the inequalities on the Tsallis relative operator entropy,the upper and lower bounds of the Tsallis relative operator entropy are derived.