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Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Renyi entropies of channels are not generally additive for p>1, we demonstrate here by a careful random selection argument that also at p=0, and consequently for sufficiently small p, there exist counterexamples.
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C. King, “Maximization of capacity and p-norms for some product channels”, arXiv:quant-ph/0103086 (2001)
2001
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P. W. Shor, “Additivity of the classical capacity of entanglement-breaking quantum channels”, J. Math. Phys. 43
2002
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C. King, “Additivity for unital qubit channels”, J. Math. Phys. 43
2002
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A. S. Holevo, R. F. Werner, “Counterexample to an additivity conjecture for output purity of quantum channels”, J. Math. Phys. 43
2002
Cited alongside, same era.
C. King, “The capacity of the quantum depolarizing channel”, IEEE Trans. Inf. Theory 49
2003
Cited alongside, same era.
R. Alicki, M. Fannes, “Note on Multiple Additivity of Minimal Rényi Entropy Output of the Werner-Holevo Channels”, Open Systems Inf. Dyn 11
2004
Cited alongside, same era.
P. Hayden, D. Leung, A. Winter, “Aspects of generic entanglement”, Comm. Math. Phys. 265
2006
Cited alongside, same era.
C. King, announced at the 1st joint AMS-PTM meeting, Warsaw 31 July – 3 Aug 2007
2007
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2007
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