On channels with positive quantum zero-error capacity having vanishing n-shot capacity

On channels with positive quantum zero-error capacity having vanishing n-shot capacity We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n, we explicitly construct low-dimensional quantum channels (input dimension 4, Choi rank 2 or 4) whose quantum zero-error capacity is positive, but the corresponding n-shot capacity is zero. We give estimates for quantum zero-error capacity of such channels as a function of n and show that these channels can be chosen in any small vicinity (in the $$cb$$ c b -norm) of a classical–quantum channel. Mathematically, this property means appearance of an ideal (noiseless) subchannel only in sufficiently large tensor power of a channel. Our approach (using special continuous deformation of a maximal commutative $$*$$ ∗ -subalgebra of $$M_4$$ M 4 ) also gives low-dimensional examples of the superactivation of 1-shot quantum zero-error capacity. Finally, we consider multi-dimensional construction which increases the estimate for quantum zero-error capacity of channels having vanishing n-shot capacity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On channels with positive quantum zero-error capacity having vanishing n-shot capacity

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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1014-0
Publisher site
See Article on Publisher Site

Abstract

We show that unbounded number of channel uses may be necessary for perfect transmission of quantum information. For any n, we explicitly construct low-dimensional quantum channels (input dimension 4, Choi rank 2 or 4) whose quantum zero-error capacity is positive, but the corresponding n-shot capacity is zero. We give estimates for quantum zero-error capacity of such channels as a function of n and show that these channels can be chosen in any small vicinity (in the $$cb$$ c b -norm) of a classical–quantum channel. Mathematically, this property means appearance of an ideal (noiseless) subchannel only in sufficiently large tensor power of a channel. Our approach (using special continuous deformation of a maximal commutative $$*$$ ∗ -subalgebra of $$M_4$$ M 4 ) also gives low-dimensional examples of the superactivation of 1-shot quantum zero-error capacity. Finally, we consider multi-dimensional construction which increases the estimate for quantum zero-error capacity of channels having vanishing n-shot capacity.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 21, 2015

References

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