Theoretical Researches On Quantum Teleportation

Quantum cryptograph is known as a kind of new communication technology, which has been developed for about 20 years. The security of quantum communication is guaranteed by the basic principles in quantum mechanics, such as the no-cloning theorem for an unknown state, Heisenberg uncertainty principle, the reliably non-distinguishing attribute of non-orthogonal quantum states. The security threat of classical cryptography is that the information has not been detected but been deciphered, which causes severe consequences. Being different from classical cryptography, the security of quantum cryptograph is not based on the computational complexity, but rooted in quantum physical mechanics, which ensures more information predominated by correspondents rather than eavesdroppers. Quantum teleportation and dense coding are two important branches of quantum information. Unknown quantum states can be sent from distant sender to receiver by using classical communication in quantum teleportation, while quantum dense coding can transform classical bits information by using quantum channel.In the paper, we firstly introduce the basic theories of quantum teleportation and dense coding. Afterwards, the main results are demonstrated as follows:â… . The relationship of teleportation and transformation operators:(1) Firstly, we discuss a scheme for teleportation of a three-particle entangled W state via a two-particle and a three-particle entangled state. Then, in accordance with the principle of superposition and transformation operators, the total state is expanded by Bell bases and the teleportation can be realized. The relation of transformation operators with unitary operation is discussed. The necessary condition to realize the teleportation is that the transformation operators have inverse operators.(2) The relationship between teleportation of a d-level n-particle state and transformation operators is discussed by using partially entangled states and d-level n+1-particle state as quantum channel, respectively. In accordance with the principle of superposition and transformation operators, the total system can be expanded by generalized Bell bases. The relation of transformation operators and unitary operation is discussed. The necessary condition to realize the teleportation is that the transformation operators have inverse operators. Furthermore, the comparison of merits and demerits for the two protocols is studied.â…¡. Perfect teleportation and dense coding:(1) We propose a kind of special multi-qubit entanglement channel, which can be utilized for perfect teleportation of an arbitrary single qubit and the state x|0>(?)N+y|1>(?)N. Various schemes are devised for perfect teleportation. We later show that the states can be utilized for dense coding as well. It can be seen that the receiver can obtain N classical bits from the sender by transmitting N-1 qubits.(2) We investigate the necessary and sufficient conditions that an entangled channel of n-qubits should satisfy to carry out perfect teleportation of an arbitrary single qubit state and dense coding. It is shown that the sender can transmit two classical bits of information by sending one qubit.(3) The case of high-dimension quantum state is also considered. Utilizing n-qudit state as quantum channel, it is proposed that the necessary and sufficient conditions are (d+2)(d-1)/2 in all to teleport an arbitrary single qudit state. The sender can transmit 2log2d classical bits of information to the receiver conditioned on the constraints.