The maximal pnorm multiplicativity conjecture is false
Abstract
For all 1 < p < 2, we demonstrate the existence of quantum channels with nonmultiplicative maximal pnorms. Equivalently, the minimum output Renyi entropy of order p of a quantum channel is not additive for all 1 < p < 2. The violations found are large. As p approaches 1, the minimum output Renyi entropy of order p for a product channel need not be significantly greater than the minimum output entropy of its individual factors. Since p=1 corresponds to the von Neumann entropy, these counterexamples demonstrate that if the additivity conjecture of quantum information theory is true, it cannot be proved as a consequence of maximal pnorm multiplicativity.
 Publication:

arXiv eprints
 Pub Date:
 July 2007
 arXiv:
 arXiv:0707.3291
 Bibcode:
 2007arXiv0707.3291H
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 Merged into arXiv:0807.4753, which is published as Comm. Math. Phys. 284(1)263280, 2008