Probabilistic Teleportation And Probabilistic Controlled Teleportation Of Multi-qubit Quantum States

In 1993, Bennett et al first proposed a protocol for teleporting an unknown pure state based on dual usage of classical and quantum channels. From then on, more and more research groups focus their attention on the topic and dramatic progress has been made in both theory and experiment. This thesis investigates the basic theory of quantum teleportation and makes a review of traditional schemes for single qubit and multi-qubit teleportation. On such a basis, we discuss the determinate and probabilistic teleportation schemes for arbitrary multi-qubit quantum states between two agents (sender Alice and receiver Bob) and then extend traditional schemes to the networked multi-agent teleportation. We first study the differences between the two main models of many-agent teleportation (quantum secret sharing and controlled teleportation). Then we discuss the determinate controlled teleportation of a triplet GHZ state and the probabilistic controlled teleportation of a triplet W state and a N-qubit GHZ state via the control of many agents in a network. Lastly, we make a summary and give an outlook of the fantastic topic.The original quantum teleportation means that the sender Alice transmits an unknown single qubit stateψto the distant receiver Bob, which enables the target qubit (in Bob's site) to be the very state ofψ. Note that what the special procedure transmit is only the information of Alice's qubit state, while the original qubit remains in Alice's site. Due to the uncertain principal and the no-cloning theorem of quantum mechanics, one cannot make exact copy and directly extract full information from the original state. Therefore, it requires division of the quantum state into two parts: classical information and quantum information, which are transmitted through classical channel and quantum channel, respectively. According to these message, Bob can configure all information of the original state into the target qubit of Bob's. In the scheme for teleporting an arbitrary N -qubit state, N independent non-maximally GHZ triplets are used as quantum channels, which avoids introducing extra auxiliary qubit. After N times similar repeats, teleportation is faithfully realized with the total possibility PN = 2N∏iN =1| di|2 .Quantum secret sharing is a"one to many"teleportation protocol, demanding a message distributed among many spatially-separated agents in a network. Thus no subset of the agents is sufficient to fully read the message but the entire set is. Moreover, anyone of the agents can be a candidate of receiver, but only one of them becomes a real one. Different from quantum secret sharing, controlled teleportation is a"one to one"(sender Alice to receiver Bob) teleportation protocol under the control of many agents. In the scheme for controlled teleportation of an arbitrary N-qubit GHZ state, the task of control is realized by each agent's projection measurement. The receiver Bob can predict where the useful information is finally stored according to even or odd number of"1"s from these projection measurements. Then Bob performs a common collective unitary transformation U to pick the smallest coefficient for all possible states. At last, Bob operatesσtransformation to adjust the basis in terms of Alice's Bell state measurement results. The total probability of successful teleportation is 2 1∏12=+ ?Nk kN ma . In the special case of using maximally entangled quantum channels, the total possibility of successful teleportation is 21 ? m via the control of m agents.