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Completely positive classical structures and sequentializable quantum protocols

Author(s): Chris Heunen | Sergio Boixo

Journal: Electronic Proceedings in Theoretical Computer Science
ISSN 2075-2180

Volume: 95;
Issue: Proc. QPL 2011;
Start page: 91;
Date: 2012;
Original page

We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with commuting Kraus operators can be sequentialized. Hence such protocols are precisely as robust under general dephasing noise when entangled as when sequential.
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