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Abstract
Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Despite some recent proposals, it still faces a fundamental problem: how to quantify its presence? In this work, we provide a universal framework for quantifying contextuality. We conduct two complementary approaches: (i) the bottom-up approach, where we introduce a communication game, which grasps the phenomenon of contextuality in a quantitative manner; (ii) the top-down approach, where we just postulate two measures, relative entropy of contextuality and contextuality cost, analogous to existent measures of nonlocality (a special case of contextuality).We then match the two approaches by showing that the measure emerging from the communication scenario turns out to be equal to the relative entropy of contextuality. Our framework allows for the quantitative, resource-type comparison of completely different games. We give analytical formulas for the proposed measures for some contextual systems, showing in particular that the Peres-Mermin game is by order of magnitude more contextual than that of
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Authors (8)
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Andrzej Grudka
- Um w Poznaniu Wydział Fizyki
-
Karol Horodecki
- Uniwersytet Gdański Wydział Informatyki
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Michał Horodecki
- Uniwersytet Gdański Wydział Fizyki
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Ryszard Horodecki
- Uniwersytet Gdański Wydział Fizyki
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P. Joshi
- Uniwersytet Gdański Wydział Fizyki
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Waldemar Kłobus
- Uniwersytet Poznań .
-
Antoni Wójcik
- Uniwersytet Poznań .
Cite as
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Keywords
Details
- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
PHYSICAL REVIEW LETTERS
no. 112,
pages 1 - 5,
ISSN: 0031-9007 - Language:
- English
- Publication year:
- 2014
- Bibliographic description:
- Grudka A., Horodecki K., Horodecki M., Horodecki P., Horodecki R., Joshi P., Kłobus W., Wójcik A.: Quantifying Contextuality// PHYSICAL REVIEW LETTERS. -Vol. 112, nr. 120401 (2014), s.1-5
- DOI:
- Digital Object Identifier (open in new tab) 10.1103/physrevlett.112.120401
- Verified by:
- Gdańsk University of Technology
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