Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1

Details Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1 Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1

2008-07-30

arxiv.org/abs/0807.4753v1

Comm. Math. Phys. 284(1):263-280, 2008.

Physics

Quantum Physics

Merger of arXiv:0707.0402 and arXiv:0707.3291 containing new and improved analysis of counterexamples. 17 pages

Scientific paper

10.1007/s00220-008-0624-0

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p >1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, 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 any channel-independent guarantee of maximal p-norm multiplicativity. We also show that a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2.

Affiliated with

Also associated with

No associations

Rating

Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-258928