The maximum output p-norm of quantum channels is not multiplicative for any p>2
Abstract
Description
We prove the claim made in the title by showing that approximately randomising maps of large dimension are counterexamples to the multiplicativity conjecture.
Superseded by arXiv:0807.4753! -- Old comment: Four pages only. If you write to me, please don't tell me how simple and obvious it is - I know that myself. I accept suggestions for journals to submit to, though; the obscurer the better. V2 has some corrections, and I removed one reference. Don't miss the more recent work arXiv:0707.3291
Superseded by arXiv:0807.4753! -- Old comment: Four pages only. If you write to me, please don't tell me how simple and obvious it is - I know that myself. I accept suggestions for journals to submit to, though; the obscurer the better. V2 has some corrections, and I removed one reference. Don't miss the more recent work arXiv:0707.3291