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Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit Formula | IEEE Journals & Magazine | IEEE Xplore

Additive Bounds of Minimum Output Entropies for Unital Channels and an Exact Qubit Formula


Abstract:

We find an upper bound for the minimum output entropy of a unital quantum channel, and obtain an exact formula for general qubit channels. Our techniques incorporate the ...Show More

Abstract:

We find an upper bound for the minimum output entropy of a unital quantum channel, and obtain an exact formula for general qubit channels. Our techniques incorporate the Rényi entropies, particularly, with Rényi parameter α = 2. Moreover, since our upper bound is additive under tensor product, we get as a corollary an upper bound for the classical capacity of unital quantum channels. Interestingly, our upper bound for the classical capacity depends only on the operator norm of matrix representations of channels on the space of traceless Hermitian operators, and is tight in the sense that it gives the precise quantity of classical capacity of the Werner-Holevo channel. As an example, we study quantum channels with operator sum representation that is made of the discrete Weyl operators (generalized Pauli operators), and explain how our formula works in this case. Finally, we find new examples for which the minimum output Rényi 2-entropy is additive.
Published in: IEEE Transactions on Information Theory ( Volume: 63, Issue: 3, March 2017)
Page(s): 1818 - 1828
Date of Publication: 19 December 2016

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