Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Mathematical Notes

Structure of the algebra generated by a noncommutative operator graph which demonstrates the superactivation phenomenon for zero-error capacity

Grigori Gennadievich Amosov, Il'ya Yur'evich Zhdanovskiy

Published May 1, 2016• 5 citations
Publisher
DOI
10.1134/s000143461605031x

Related papers

On superactivation of zero-error capacities of a quantum channel and its implications

Максим Евгеньевич Широков, Tatiana Shulman

•Sep 10, 2013•0 citations

On Superactivation of Zero-Error Capacities and Reversibility of a Quantum Channel

Максим Евгеньевич Широков, Tatiana Shulman

arXiv:1309.2610•Communications in Mathematical Physics•Mar 4, 2015•30 citations

Algorithmic superactivation of asymptotic quantum capacity of zero-capacity quantum channels

László Gyöngyösi, Sándor Imre

arXiv:1207.4491•Information Sciences•Aug 24, 2012•16 citations

On inner geometry of noncommutative operator graphs

Grigori Gennadievich Amosov

The European Physical Journal Plus•Oct 1, 2020•2 citations

On the structutre of the algebra generated by the non-commutative operator graph demonstrating superactivation for a zero-error capacity

Grigori Gennadievich Amosov, Il'ya Yur'evich Zhdanovskiy

Recently M.E. Shirokov introduced the non-commutative operator graph depending on the complex parameter $θ$ to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We study the algebraic structure of this graph. The relations for the algebra generated by the graph are derived. In the limiting case $θ=\pm1$ the graph becomes abelian and degenerates into the direct sum of four one-dimensional irreducible representations of the Klein group.

arXiv:1512.02096•Dec 7, 2015•0 citations

Sufficient conditions for additivity of the zero-error classical capacity of quantum channels

Jeonghoon Park, Jeong San Kim

The one-shot zero-error classical capacity of a quantum channel is the maximum amount of classical information that can be transmitted with zero probability of error via a single channel use. This capacity is fundamentally characterized by the logarithm of the independence number of the noncommutative graph induced by the quantum channel. Consequently, the additivity of the one-shot zero-error classical capacity is equivalent to the multiplicativity of the independence number of the associated noncommutative graphs. As the independence number is not multiplicative in general, the specific conditions under which multiplicativity is preserved remain an open question in quantum information theory. Here, we establish some sufficient conditions for the multiplicativity of the independence number and provide explicit examples of quantum channels that satisfy these criteria. Furthermore, we investigate the block form of noncommutative graphs and derive the conditions under which the independence number remains multiplicative within this framework. These results offer new insights into the structural properties of noncommutative graphs and the fundamental limits of zero-error quantum communication.

quant-pharXiv:2601.18538•Physical Review A•Jan 27, 2026•0 citations
Recently M.E. Shirokov introduced the non-commutative operator graph depending on the complex parameter θθθ to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We study the algebraic structure of this graph. The relations for the algebra generated by the graph are derived. In the limiting case θ=±1θ=\pm1θ=±1 the graph becomes abelian and degenerates into the direct sum of four one-dimensional irreducible representations of the Klein group.
The one-shot zero-error classical capacity of a quantum channel is the maximum amount of classical information that can be transmitted with zero probability of error via a single channel use. This capacity is fundamentally characterized by the logarithm of the independence number of the noncommutative graph induced by the quantum channel. Consequently, the additivity of the one-shot zero-error classical capacity is equivalent to the multiplicativity of the independence number of the associated noncommutative graphs. As the independence number is not multiplicative in general, the specific conditions under which multiplicativity is preserved remain an open question in quantum information theory. Here, we establish some sufficient conditions for the multiplicativity of the independence number and provide explicit examples of quantum channels that satisfy these criteria. Furthermore, we investigate the block form of noncommutative graphs and derive the conditions under which the independence number remains multiplicative within this framework. These results offer new insights into the structural properties of noncommutative graphs and the fundamental limits of zero-error quantum communication.