Quantum State Cloning, Flip, And The Theory Of Teleportation

This thesis presents my main research works carried out during my master course. In this thesis, I focus on the manipulation and transmission of quantum states and research the quantum teleportion, quantum telefliping and telecloning, quantum multiple cloning-cum-flipping, quantum multiple anti-cloning. Significant new results are shown below.1. Two schemes, using single three-particle maximal GHZ state or two EPR states as quantum channels, for deterministic teleportation of arbitrary three-particle GHZ state are proposed. These schemes are also generalized into the case of teleportation of arbitrary n ( n≥4) particles GHZ state. It is found that when using single three-particle GHZ state which is affected by noise as quantum channel, the fidelity of teleportation is only related to the entanglement of the channel; However, when using two EPR states which is affected by noise as quantum channels, the fidelity of teleportation is related to the entanglement of both the channels and the unknown state to be delivered.2. One scheme for 1â†'1 teleflipping and 1â†'2 telecloning of an arbitrary qubit is proposed. One of the three spatially separated receivers can get one orthogonal complementing state of the original unknown state with the optimal fidelity of 2/3, the other two receivers can respectively get one copy of the original unknown state with the optimal fidelity of 5/6. The scheme is also generalized into the case of 1â†'Mteleflipping and 1â†'( M+ 1) telecloning of qubit.3. One scheme, using single particular four-particle entangled state as quantum information channel, for 1â†'2 universal telecloning of an arbitrary two-particle entangled state is proposed. This scheme is generalized into the case of 1â†'N( N > 2) universal telecloning of an arbitrary two-particle entangled state. Furthermore, a scheme, using the same four-particle entangled state as quantum information channel with the assistance of multi-target-qubit C-Not gate and additional qubits, for 1â†'2 universal telecloning of an arbitrary n -particle( n≥3) GHZ state is proposed. This scheme is also generalized into the case of 1â†'N( N > 2) telecloning of an arbitrary n -particle GHZ state.4. We prove that an arbitrary nonorthogonal state randomly selected from a set can evolve into a linear superposition of multiple original and orthogonal complementing states with failure branch if and only if the input states are linearly independent. We derive a bound on the success probabilities of our machine. We show that quantum probabilistic flipping, quantum probabilistic anti-cloning, quantum probabilistic cloning and quantum probabilistic multiple anti-cloning machines are special cases of our machine. The results for a single input state are also generalized into the case of several copies of an input state. Furthermore, we prove that an arbitrary nonorthogonal state randomly selected from a set can evolve into a linear superposition of multiple copies of anti-cloned states (an orthogonal state along with the original) with failure branch if and only if the input states are linearly independent. We derive a bound on the success probabilities of our machine. We show that quantum probabilistic anti-cloning machines and quantum probabilistic multiple anti-cloning machines are special cases of our machine. The results for a single input state are also generalized into the case of several input copies of a state.