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Communications in Mathematical Physics

, Volume 284, Issue 1, pp 281–290 | Cite as

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p Close to 0

  • Toby Cubitt
  • Aram W. Harrow
  • Debbie Leung
  • Ashley Montanaro
  • Andreas Winter
Article

Abstract

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi 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.

An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Rényi entropy is non-additive for all p ≲ 0.11. We conjecture however that violations of additivity exist for all p < 1.

Keywords

Entangle State Quantum Channel Minimum Output Random Subspace Schmidt Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Toby Cubitt
    • 1
  • Aram W. Harrow
    • 2
  • Debbie Leung
    • 3
  • Ashley Montanaro
    • 2
  • Andreas Winter
    • 1
    • 4
  1. 1.Department of MathematicsUniversity of BristolBristolUK
  2. 2.Department of Computer ScienceUniversity of BristolBristolUK
  3. 3.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  4. 4.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore

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