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Capacity of quantum channels
Author: ChenXiaoYu
Tutor: ChouPeiLiang
School: Zhejiang University
Course: Communication and Information System
Keywords: Quantum channel Classic Capacity Quantum Capacity Quantum entanglement Fermi systems Gaussian channel Quantum errorcorrecting codes Coherent information Input Signal Noise channel
CLC: TN911.2
Type: PhD thesis
Year: 2002
Downloads: 396
Quote: 2
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Abstract
Gaussian quantum channel especially quantum channel capacity has important theory significance. Like classical information system is divided into analog and digital systems, the quantum system is divided into qubit systems and continuous variable systems. In all continuous variable quantum states, quantum Gaussian state the most important in practical basically contains all the experiments can be realized in a continuous variable systems. And in theory is simple, and easy to handle the issue resolved. There are two types of quantum channel capacity; One is the amount of subchannel transmit classical information, such as optical fiber transmission 0,1 string, the quantum state is known, then we talk about classical information capacity, we will discuss the first three chapters the other is the quantum channel transmission unknown quantum state, then we have to consider is the quantum information is transmitted throughout the Hilbert space, its internal state, including quantum entanglement and other parts of the phase information can not be destroyed, We will discuss in later chapters. Our research focuses on the capacity of Gaussian quantum well and the capacityrelated problems. Chapter 1 Introduction of quantum information theory, the introduction of the necessary symbols and recalled the classical quantum channel capacity of the general result. For the later application of the product are listed in the input state output when measuring entanglement classical communication capacity HolevoSchumacherWestmoreland theorem, and the sender and receiver as an auxiliary quantum entanglement between the classical communication capacity BennettShor SmolinThapliyal Theorem. Quantum systems are usually based on their statistical properties of the particles into the system and Bose Fermi systems, in the second and third chapters we will discuss Fermi electron transport capacity of the channel and the photon transmission classic Bose Classical capacity of the channel. The second chapter gives input fermion average occupation number limit (average input power limitation) under the conditions of singlemode quantum channel Fermi Classical capacity of the system. Based on quantum channel summation operator said it would singlemode Fermi quantum channel parametric system, gives the maximum value of the quantum mutual information, that is, entanglementassisted classical capacity is calculated. Chapter 3 describes the Bose quantum Gaussian states and quantum Gaussian channel. Studies and calculations of quantum entanglementassisted singlemode when the input power is limited thermal radiation noise channel to transmit classical information capacity, given the corresponding singlechannel compression problem is calculated. The thermal noise channel, indicating that the thermal capacity of the input signal reaches the noise signal, help to achieve the compression state of the channel capacity; while for compression channel capacity is generally achieved when the input compressed state. The transmission of quantum information about the content, placed fourth, fifth and sixth chapters discuss, respectively, related to quantum errorcorrecting codes, quantum capacity and quantum entanglement. The fourth chapter studies the quantum errorcorrecting codes, calculated based on the framework of group theory in quantum 8 encoding three yards of such price tag, with the quadratic residue method to find a class of two and three error correcting quantum codes. Describes the continuous variable quantum encoding. Chapter V through quantum fidelity (fidelity) of the input signal invariant under unitary transformations define the quantum binary symmetric channel. Normal product operator with the technique of integration within the mutual information obtained quantum counterpart  Coherent Information thermal noise signal with input power and channel thermal noise power represented by formula. Discussed by Holevo and Werner introduced Quantum Quantum Gaussian channel capacity upper bound and determined by the quantum coding lower bound. Quantum Gaussian channel capacity fascinating feature is the Planck constant h replaces the classical capacity constraints in the input signal power position. Chapter VI introduces quantum entanglement quantum capacity and the relationship, and then study the Gaussian quantum entanglement bilateral upper and lower limits. Gaussian mixture given quantum state of the three boundaries, with only two parameters of the heat of compression is called Gaussian state quantum states to test whether they are good upper and lower limits, and calculate the coherent state information for comparison purposes. According Horodecki et al, entangled coherent message guess is the lower limit of oneway entanglement distillation, this assumption is called hashing ranging from ntype, on the evidence noisy channel coding theorem is essential. Our results indicate that there is no direct evidence of the continuous variable systems hashing inequality is violated. Based on hashing inequality, of the infinite, compressed thermal state can calculate the relative entropy entanglement and entanglement distillation. On the other hand, the low compression side generated entanglement can be more accurately given.

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