The maximal p-norm multiplicativity conjecture is false

Patrick Hayden

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arXiv · 0707.3291

The maximal p-norm multiplicativity conjecture is false

Patrick Hayden

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Abstract

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.

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Patrick Hayden. 2007-07-23. The maximal p-norm multiplicativity conjecture is false. https://arxiv.org/abs/0707.3291

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