On the multiplicativity conjecture for quantum channels

TL;DR

This paper formulates a multiplicativity conjecture for quantum channels, linking it to the additivity problem of channel capacity, and proves it for natural number values of parameter p.

Contribution

It introduces a new multiplicativity conjecture in quantum information theory and provides a proof for natural number parameters, advancing understanding of quantum channel capacities.

Findings

Conjecture formulated for quantum channels.

Proof provided for natural number p.

Connection established with channel capacity additivity.

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 $p$.