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Leaks: Quantum, Classical, Intermediate and More

Department of Physics, Imperial College London, Kensington, London SW7 2AZ, UK
Department of Computer Science, University of Oxford, Oxford OX1 3PA, UK
Author to whom correspondence should be addressed.
Academic Editors: Giacomo Mauro D’Ariano and Paolo Perinotti
Entropy 2017, 19(4), 174;
Received: 26 January 2017 / Revised: 30 March 2017 / Accepted: 12 April 2017 / Published: 19 April 2017
(This article belongs to the Special Issue Quantum Information and Foundations)
PDF [335 KB, uploaded 19 April 2017]


We introduce the notion of a leak for general process theories and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance of which describes the emergence of classical theory by adjoining decoherence leaks to quantum theory. Finally, we show that defining a notion of purity for processes in general process theories has to make reference to the leaks of that theory, a feature missing in standard definitions; hence, we propose a refined definition and study the resulting notion of purity for quantum, classical and intermediate theories. View Full-Text
Keywords: process theory; classical limit; purity process theory; classical limit; purity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Selby, J.; Coecke, B. Leaks: Quantum, Classical, Intermediate and More. Entropy 2017, 19, 174.

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