The maximal p-norm multiplicativity conjecture is false
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.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2007
- DOI:
- 10.48550/arXiv.0707.3291
- arXiv:
- arXiv:0707.3291
- Bibcode:
- 2007arXiv0707.3291H
- Keywords:
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- Quantum Physics;
- Mathematical Physics
- E-Print:
- Merged into arXiv:0807.4753, which is published as Comm. Math. Phys. 284(1)263-280, 2008