Information transmission through a noisy quantum channel

@article{Barnum1998InformationTT,
  title={Information transmission through a noisy quantum channel},
  author={Howard Barnum and Michael A. Nielsen and Benjamin Schumacher},
  journal={Physical Review A},
  year={1998},
  volume={57},
  pages={4153-4175}
}
Noisy quantum channels may be used in many information-carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two… 

Figures from this paper

Principles of Quantum Communication Theory: A Modern Approach

TLDR
This work adopts an information-theoretic perspective throughout and gives a comprehensive account of fundamental results in quantum communication theory from the past decade, with an emphasis on the modern one-shot-to-asymptotic approach that underlies much of today's state-of-the-art research in this field.

Entanglement fidelity and measure of entanglement

TLDR
It is shown that the entangling aspect of the so called entanglement fidelity is neither of typeEntanglement of formation and concurrence nor of type negativity.

Quantum channels and memory effects

TLDR
The study of memory effects in quantum channels is a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics.

Quantum Communication Processes and Their Complexity

TLDR
Information Dynamics is a new concept unifying the dynamics of a state and the complexity of the system itself, which can discuss in a unified frame the problems such as in mathematics, physics, biology, information science.

Distillation of secret key and entanglement from quantum states

  • I. DevetakA. Winter
  • Computer Science
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2005
TLDR
A coding theorem is proved to achieve the ‘wire–tapper’ bound, the difference of the mutual information Alice–Bob and that of Alice–Eve, for so–called classical–quantum-quantum–correlations, via one–way public communication, which yields information–theoretic formulae for the distillable secret key.

Fundamentals of quantum information theory

Purifying Noisy Entanglement Requires Collective Measurements

Known entanglement purification protocols for mixed states use collective measurements on several copies of the state in order to increase the entanglement of some of them. We address the question of

On quantum fidelities and channel capacities

TLDR
It is shown that a restricted class of encodings is sufficient to transmit any quantum source which may be transmitted on a given channel, and that the availability of an auxiliary classical channel from encoder to decoder does not increase the quantum capacity.

The platypus of the quantum channel zoo

TLDR
A remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features is studied; the simplest example from this family, a qutrit-to-qutrit channel intuitively obtained by hybridizing together a simple degradable channel with a completely useless qubit channel is studied.
...

References

SHOWING 1-10 OF 23 REFERENCES

Linear Algebra and Its Applications 10

  • 285
  • 1975

Phys

  • Rev. A 54, 2629
  • 1996

Phys

  • Rev. A 54, 2614
  • 1996

Optics 41

  • 2343
  • 1994

Optics 41

  • 2315
  • 1995

The Structure and Interpretation of Quantum Mechanics

Preface Introduction. The Stern-Gerlach Experiment PART I THE STRUCTURE OF QUANTUM THEORY 1. Vector Spaces Vectors Operators Eigenvectors and Eigenvalues Inner Products of Vectors in R2 Complex

A survey of matrix theory and matrix inequalities

The mathematical theory of communication

TLDR
This commemorative reprinting of The Mathematical Theory of Communication, published originally as a paper on communication theory more than fifty years ago, is released.

A Survey of Matrix Theory and Matrix Inequalities

TLDR
This book presents an enormous amount of information in a concise and accessible format and begins with the assumption that the reader has never seen a matrix.