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Problems of Information Transmission

On a Sufficient Condition for Additivity in Quantum Information Theory

Nilanjana Datta, Alexander Semenovich Holevo, Yu. M. Suhov

Published Apr 1, 2005• 11 citations
Publisher
DOI
10.1007/s11122-005-0013-7

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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.
The Pauli Exclusion Principle ensures that orbital occupations arise from a physically real- istic quantum system. There are additional conditions, motivated by quantum information theory, that are necessary for electron occupations to arise out of pure quantum states that are said to generalize the Pauli principle. Our work with Generalized Pauli conditions has lead us to develop electronic structure theories that are able to, i) recover many-body correla- tion energies, ii) derive sufficient conditions for openness in a quantum system, iii) formulate a geometric perspective on energy transfer, and, iv) highlight the structural complexity of excited state spectra, from one-electron theories.