Counterexamples to the Maximal pNorm Multiplicativity Conjecture for all p > 1
Abstract
For all p > 1, we demonstrate the existence of quantum channels with nonmultiplicative maximal output pnorms. Equivalently, for all p > 1, the minimum output Rényi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Rényi 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 any channelindependent guarantee of maximal pnorm multiplicativity. We also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 November 2008
 DOI:
 10.1007/s0022000806240
 arXiv:
 arXiv:0807.4753
 Bibcode:
 2008CMaPh.284..263H
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory;
 Mathematical Physics
 EPrint:
 Merger of arXiv:0707.0402 and arXiv:0707.3291 containing new and improved analysis of counterexamples. 17 pages