Communications in Mathematical Physics

, Volume 328, Issue 3, pp 995–1021 | Cite as

Asymptotically Well-Behaved Input States Do Not Violate Additivity for Conjugate Pairs of Random Quantum Channels

  • Motohisa Fukuda
  • Ion Nechita


It is now well-known that, with high probability, the additivity of minimum output entropy does not hold for pairs of the random quantum channel and its complex conjugate. We investigate asymptotic behavior of output states of r-tensor powers of such pairs, as the dimension of inputs grows. We compute the limit output states for any sequence of well-behaved inputs, which consist of a large class of input states having a nice set of parameters. Then, we show that among these input states tensor products of Bell states give asymptotically the least output entropy, giving positive mathematical evidence towards additivity of above pairs of channels.


Quantum Channel Input State Bell State Conjugate Pair Permutation Matrice 
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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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Zentrum Mathematik, M5Technische Universität MünchenGarchingGermany
  2. 2.CNRS, Laboratoire de Physique Théorique, IRSAMCUniversité de Toulouse, UPSToulouseFrance

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