Study Of Remote State Preparation In Quantum Information Theory

Quantum information science is a inter-discipline,which concerns physics,math and com-puter science. The main subject of quantum information science is the information transmission and processing tasks,which are based on quantum systems. Some tasks are unachievable in the classical information frame or lack efficient ways to handle. So, when compare with classical information, quantum information shows its advantages in these tasks. From the 90s of the last century, people have obtained lots of remarkable results in this field, including .quantumteleporta-tion, quantum cryptography, remote state preparation, quantum super dense coding and quantum private key distribution. Recently, quantum communication is getting increasingly widespread attention. On one hand, it's because quantum communication can make the transmission of infor-mation safer and more efficient. On the other hand this discipline has gradually developed from theory and experiment to practical application and industrialization.As a carrier of information, quantum state plays a key role in quantum information transmis-sion and processing. The most commonly seen mathematical model of quantum state is quantum bit (or qubit). In contrast to the classical information concept of bit, which can represent only two states, i.e., 0 or 1, the qubit can represent any superposition state between 0 and 1. Also, when we have a multi-qubit system,the quantum entanglement may be established. If one qubit collapse the some state, the other qubit(s) will collapse to the relating state simultaneously. Based on these characteristics of quantum states, quantum communication features qualitative improvements in security and efficiency over classical communication. For the information security, because any attempt of extracting information from a quantum state will inevitably alter the original quantum state, so any eavesdropping can be detected by the communicators, giving them a chance to ter-minate the insecure communication. For the communication efficiency, using the pre-established quantum entanglement pairs, quantum superdense coding can help the receiver extract two bits classical information by sending him only one bit of classical information from the sender,which doubles the communication efficiency. When extended to a higher dimension, the concept of qubit can be extended to qutrit (three-dimensional), qudit (d-dimensional), and so on. But no matter what dimensions of the quantum states are, the preparations and transmission of them are always the first thing to be considered in any quantum communication process.In quantum information theory, quantum teleportation and remote state preparation are two most notable protocols utilizing quantum entanglement and classical information. Both protocols combine the processes of quantum state preparation and quantum state transmission, in order to achieve the purpose of transmitting quantum information. The differences of these two protocols are as follows: First, in the quantum teleportation the sender Alice has a physical sample of the target quantum state, but she may not know what the exact state is, i.e. she may not know the mathematical expression of the target state. While in the remote state preparation, the sender doesn't have the physical sample of the target state, but she knows the exact expression of it.Second, when perform the faithful quantum teleportation, a maximally entangled two-qubit stateand two classical bits communication are both necessary resource to be consumed. While in the faithful remote state preparation, the entanglement and the classical communication needed are trade-off resources, which means the increase in one will can decrease the consumption of the other resource. In this paper we will give the comparison between these two protocols, and based on our work, we will give some profound theoretical results under different remote state preparation schemes.Our main results are listed as follows:First, we study the unfaithful quantum teleportation and remote state preparation. By investi-gating the similar to Standard Quantum Teleportation Scheme and the similar to Pati RSP scheme,we obtain some profound results on the enhancibility of the fidelity of the unfaithful quantum tele-portation and remote state preparation.Then, based on a constructive scheme proposed by Berry, which can be used for remotely preparing a general pure state using a pure entangled state and finite classical communication, we provide an optimization procedure. Our procedure can be used to minimize the classical com-munication cost in preparing a general pure qubit, thus solving the classical information over-consumption problem in Berry 's scheme when preparing a general pure qubit. Interestingly, our optimization procedure is linked to the uniform arrangement of N points on the Bloch sphere,which provides a geometric description.Another aspect of our work is we propose a deterministic remote state preparation scheme for preparing an arbitrary (including pure and mixed) qubit, where a partially entangled state and finite classical communication are used. To our knowledge, our scheme is the first RSP scheme that fits into this category. As mentioned before, the RSP scheme proposed by Berry can only be used to prepare an arbitrary pure qubit. Even so, our scheme saves classical communication by approximate 1 bit per prepared qubit under equal conditions. When using a maximally entangled state, the classical communication for our scheme is 2 bits, which agrees with Lo' s conjecture on the resource cost. Furthermore Alice can switch between our RSP scheme and a Standard Quantum Teleportation Scheme without letting Bob know, which makes the quantum channel multipurpose.