On the multiplicativity conjecture for quantum channels

Abstract

A multiplicativity conjecture for quantum communication channels is formulated, validity of which for the values of parameter $p$ close to 1 is related to the solution of the fundamental problem of additivity of the channel capacity in quantum information theory. The proof of the conjecture is given for the case of natural numbers $p$.

7 pages, LATEX, no figures

References in corpus (2)

• Coding Theorems for Quantum Channels
• On some additivity problems in quantum information theory

Cited by in corpus (17)

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• Remarks on additivity of the Holevo channel capacity and of the entanglement of formation
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• Scalable programmable quantum gates and a new aspect of the additivity problem for the classical capacity of quantum channels
• The maximal p-norm multiplicativity conjecture is false
• A quantum channel with additive minimum output entropy
• Conditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p
• A Note on the p->q norms of Completely Positive Maps
• Multiplicativity of Maximal p-Norms in Werner-Holevo channels for $1\le p\le 2$
• Comments on multiplicativity of maximal p-norms when p = 2
• New multiplicativity results for qubit maps
• Remark on the additivity conjecture for the quantum depolarizing channel
• A Norm Compression Inequality for Block Partitioned Positive Semidefinite Matrices
• Multiplicativity of Accessible Fidelity and Quantumness for Sets of Quantum States
• There, and Back Again: Quantum Theory and Global Optimisation
• Analysis of the Entanglement Cost and Calculation of the Holevo Capacity
• Multiplicativity properties of entrywise positive maps