دانلود کتاب نظریه ریاضی پروتکل‌های تله‌پورت کوانتومی

This book is written with an objective of providing a theoretical as well as mathematical introduction to the concept of teleportation in a self-contained manner. The required mathematics and physics is described at the beginning. The description starts from the elementary level and is restricted to the minimum required for serving the purpose of the book without making any compromise with rigor. This is done with a view to making the book accessible to scientists and engineers without having a specialized knowledge in physics, applied mathematics or computer science. The book is divided into three parts. The contents of these three parts are concisely as follows. In the first part the requisite background materials are given. It is a selfcontained presentation. The mathematics is presented from the preliminary level and includes everything which is required for the understanding of the subject matter contained in the book. The requisite part of quantum mechanics is also described in a self-contained way. It is better that the reader has an introductory knowledge of quantum mechanics, but this is not necessary. The topics of quantum physics covered include qubits, multiqubit systems, entanglement, quantum evolution, quantum noise, quantum measurement and a general description of quantum communication system. The mathematics discussed here includes linear space, Hilbert space, linear operators in general, Hermitian operators, unitary operators, projection operators, tensor products and the partial trace operations. There are several illustrations on the topics included in this part. In the second part the topics are teleportation protocols for different types of states using appropriate entangled quantum resources as channels. There are several versions of teleportation like controlled teleportation, multi-hop teleportation, probabilistic teleportation etc. whose final aim is to transfer quantum states with the help of entanglement resources. The abovementioned variations are described in this section. The third part of this book is dedicated to the analysis of teleportation protocols through noisy channels. Noise is an inalienable phenomena in every communication system. We consider quantum noise affecting the entangled communication channel. This noise is modeled through Kraus operators. Four types of noises are considered, namely, Amplitudedamping, Bit-flip, Phase-flip and Phase-damping noise. In this part we analyze the effects of these noises on the concerned teleportation protocols by calculating the fidelity of the process. Fidelity is a measure by which we understand the deviation of the quantum state actually obtained at the receiver’s end from that which was originally intended for transfer. Further it is important to control the effect of noise as far as possible. We present in this part weak and reversal measurements and environment assisted measurements as methods for such control.