Abstract

Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. Here we review the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels.

Highlights

  • A CCORDING to Moore’s Law [322], the physical limitations of classical semiconductor-based technologies could be reached within the few years

  • 1) Discussion: Before starting the discussion on various capacities of quantum channels and the related consequences we summarize the basic definitions and formulas of quantum information theory intended to represent the information stored in quantum states

  • 2) Density Matrix and Trace Operator: we introduce a basic concept of quantum information theory, called the density matrix

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Summary

A Survey on Quantum Channel Capacities

Laszlo Gyongyosi , Member, IEEE, Sandor Imre, Senior Member, IEEE, and Hung Viet Nguyen, Member, IEEE. Abstract—Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. Many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. We review the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels

INTRODUCTION
Applications and Gains of Quantum Communications
Privacy and Performance Gains of Quantum Channels
Communication Over a Quantum Channel
Formal Model
Quantum Channel Capacity
Definitions
Geometrical Interpretation of the Density Matrices
Channel System Description
Related Work
CLASSICAL CAPACITIES OF A QUANTUM CHANNEL
Extended Formal Model
Capacity of Classical Channels
Transmission of Classical Information Over Noisy Quantum Channels
The Private Classical Capacity
The Entanglement-Assisted Classical Capacity
The Classical Zero-Error Capacity
Entanglement-Assisted Classical Zero-Error Capacity
THE QUANTUM CAPACITY OF A QUANTUM CHANNEL
Preserving Quantum Information
Quantum Coherent Information
Connection Between Classical and Quantum Information
The Lloyd-Shor-Devetak Formula
The Assisted Quantum Capacity
The Zero-Error Quantum Capacity
Relation Between Classical and Quantum Capacities of Quantum Channels
Channel Maps
Capacities
Realistic Material
Acting Time in Asymmetric Channels
Implementation of Quantum Channel in FSO-Based Quantum Key Distribution
Quantum Channel Codes for Approaching Quantum Channel Capacity
Quantum Network Coding for Entanglement Distribution
CONCLUSION
Partial Trace
Findings
Quantum Entanglement
Fidelity
Full Text
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