| Additivity Conjectures |
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Description The so-called additivity-conjectures of quantum information theory concern the mathematical proprty of extensivity of a number of entropic parameters associated to channels and (bipartite) quantum states: the minimum output entropy, the Holevo-quantity and the entanglement of formation, among others. All of them are long conjectured to be additive (extensive) for tensor products of channels/states -- in fact, Shor showed in 2002 that all their additivities are equivalent. However, recently new doubts about these conjectures arose when examples were found where the minimum p-Renyi output entropy of channels is not additive, for p>1, and then even some p<1. This project will investigate these counterexamples further, find new ones and attempt to make progress with the original conjecture (limiting case of p=1). CQT people involved in the project Andreas Winter Publications
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