2007/07/23 by Patrick Hayden · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP
published as Merged into arXiv:0807.4753, which is published as Comm. Math. Phys. 284(1)263-280, 2008
arxiv created 2007/07/23 · arxiv updated 2011/10/25
For all 1 < p < 2, we demonstrate the existence of quantum channels with non-multiplicative maximal p-norms. 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 p-norm multiplicativity.