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Entropy in general physical theories

Short, Anthony J. and Wehner, Stephanie (2010) Entropy in general physical theories. New Journal of Physics, 12 . 033023. ISSN 1367-2630.

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Information plays an important role in our understanding of the physical world. Hence we propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical worlds, our measure reduces to the von Neumann and Shannon entropies, respectively. It can even be used in a quantum or classical setting where we are only allowed to perform a limited set of operations. In a world that admits superstrong correlations in the form of non-local boxes, our measure can be used to analyze protocols such as superstrong random access encodings and the violation of 'information causality'. However, we also show that in such a world no entropic measure can exhibit all the properties we commonly accept in a quantum setting. For example, there exists no 'reasonable' measure of conditional entropy that is subadditive. Finally, we prove a coding theorem for some theories that is analogous to the quantum and classical settings, providing us with an appealing operational interpretation.

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Additional Information:© 2010 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Issue 3 (March 2010): received 15 October 2009; published 15 March 2010. The non-local game used in our example above was discovered in collaboration with Andrew Doherty, whom we thank for his kind permission to use it here. The authors also thank Sergio Boixo, Matthew Elliot and Jonathan Oppenheim for interesting discussions, and Matt Leifer and Ronald de Wolf for comments on an earlier draft. SW is supported by NSF grants PHY- 04056720 and PHY-0803371. AJS is supported by a Royal Society URF, and in part by the EU QAP project (CT-015848). Part of this work was done while AJS was visiting Caltech (Pasadena, USA). Note added. During the course of this work, we learned that an independent work on the same general topic [40] is to appear in New Journal of Physics. Yet another related work appeared subsequently [41].
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EU QAP projectCT-015848
Classification Code:PACS: 03.67.Hk; 89.70.-a; 84.40.Ua; 03.65.Ta
Record Number:CaltechAUTHORS:20100406-114048485
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Official Citation:Anthony J Short and Stephanie Wehner 2010 New J. Phys. 12 033023 doi: 10.1088/1367-2630/12/3/033023
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17875
Deposited By: Jason Perez
Deposited On:08 Apr 2010 15:56
Last Modified:03 Oct 2019 01:34

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