Non-Additivity in Classical-Quantum Wiretap Channels

@article{Tikku2020NonAdditivityIC,
  title={Non-Additivity in Classical-Quantum Wiretap Channels},
  author={Arkin Tikku and Mario Berta and Joseph M. Renes},
  journal={IEEE Journal on Selected Areas in Information Theory},
  year={2020},
  volume={1},
  pages={526-535}
}
Due to Csiszár and Körner, the private capacity of classical wiretap channels has a single-letter characterization in terms of the private information. For quantum wiretap channels, however, it is known that regularization of the private information is necessary to reach the capacity. Here, we study hybrid classical-quantum wiretap channels in order to resolve to what extent quantum effects are needed to witness non-additivity phenomena in quantum Shannon theory. For wiretap channels with… 

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References

SHOWING 1-10 OF 39 REFERENCES

Structured codes improve the Bennett-Brassard-84 quantum key rate.

It is shown that a conjectured single-letter formula for quantum key distribution, Bennnett-Brassard-84, is false, uncovering a deep ignorance about good private codes and exposing unfortunate complications in the theory of QKD.

How to differentiate between non-orthogonal states

Quantum privacy and quantum wiretap channels

This work argues that in the definition of the so-called “quantum privacy,” Holevo quantities should be used instead of classical mutual informations and shows that this modified quantum privacy is the optimum achievable rate of secure transmission.

One-way quantum key distribution: Simple upper bound on the secret key rate

A simple method to obtain an upper bound on the achievable secret key rate in quantum key distribution (QKD) protocols that use only unidirectional classical communication during the public-discussion phase and can be formulated as a semidefinite program, which can be efficiently solved.

Information Theory - Coding Theorems for Discrete Memoryless Systems, Second Edition

This new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics.

On the Evaluation of Marton’s Inner Bound for Two-Receiver Broadcast Channels

Improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region are established and lead to a proof that a randomized-time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels.

Quantum privacy and quantum wiretap channels

This work argues that in the definition of the so-called “quantum privacy,” Holevo quantities should be used instead of classical mutual informations and shows that this modified quantum privacy is the optimum achievable rate of secure transmission.

-convexity

Given a homeomorphism one can define on the topological space X a set operator through the formula . Such a convexity on X has all the topological, geometric and algebraic properties of the usual

Quantum Information Theory

The author develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication.