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Constructing Quantum Network Coding Schemes from Classical Nonlinear Protocols | | Hirotada Kobayashi
; François Le Gall
; Harumichi Nishimura
; Martin Roetteler
; | | Date: |
21 Dec 2010 | | Abstract: | The k-pair problem in network coding theory asks to send k messages
simultaneously between k source-target pairs over a directed acyclic graph. In
a previous paper [ICALP 2009, Part I, pages 622--633] the present authors
showed that if a classical k-pair problem is solvable by means of a linear
coding scheme, then the quantum k-pair problem over the same graph is also
solvable, provided that classical communication can be sent for free between
any pair of nodes of the graph. Here we address the main case that remained
open in our previous work, namely whether nonlinear classical network coding
schemes can also give rise to quantum network coding schemes. This question is
motivated by the fact that there are networks for which there are no linear
solutions to the k-pair problem, whereas nonlinear solutions exist. In the
present paper we overcome the limitation to linear protocols and describe a new
communication protocol for perfect quantum network coding that improves over
the previous one as follows: (i) the new protocol does not put any condition on
the underlying classical coding scheme, that is, it can simulate nonlinear
communication protocols as well, and (ii) the amount of classical communication
sent in the protocol is significantly reduced. | | Source: | arXiv, 1012.4583 | | Services: | Forum | Review | PDF | Favorites | |
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