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Abstract
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 Rényi entropy of order p of a quantum channel is not additive. The violations found are large; in all cases, the minimum output Rényi 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.
Original language | English |
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Pages (from-to) | 263 - 280 |
Number of pages | 18 |
Journal | Communications in Mathematical Physics |
Volume | 284 |
Issue number | 1 |
DOIs | |
Publication status | Published - Nov 2008 |
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Dive into the research topics of 'Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p >1'. Together they form a unique fingerprint.Projects
- 1 Finished
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RANDOM & NONRANDOM CODING FOR QUANTUM INFORMATION
Winter, A. J. (Principal Investigator)
1/10/06 → 1/10/11
Project: Research