Non-signaling boxes and quantum logics,

Using a quantum logic approach we analyze the structure of the so-called non-signaling theories respecting relativistic causality, but allowing correlations violating bounds imposed by quantum mechanics such as CHSH inequality. We discuss the relations among such theories, quantum mechanics, and classical physics. Our main result is the construction of a probability theory adequate for the simplest instance of a non-signaling theory—the two non-signaling boxes world—in which we exhibit its differences in comparison with classical and quantum probabilities. We show that the question of whether such a theory can be treated as a kind of 'generalization' of the quantum theory of the two-qubit system cannot be answered positively. Some of its features put it closer to the quantum world—on the one hand, for example, the measurements are destructive, though on the other hand the Heisenberg uncertainty relations are not satisfied. Another interesting property contrasting it from quantum mechanics is that the subset of 'classically correlated states', i.e. the states with only classical correlations, does not reproduce the classical world of the two two-state systems. Our results establish a new link between quantum information theory and the well-developed theory of quantum logics.
Keywords quantum mechanics  nonsignaling theories  quantum probability
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,035
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Mechanics: Non-Classical, Non-Quantum.Elliott Tammaro - 2012 - Foundations of Physics 42 (2):284-290.
From Physics to Information Theory and Back.Wayne C. Myrvold - 2010 - In Alisa Bokulich & Gregg Jaeger (eds.), Philosophy of Quantum Information and Entanglement. Cambridge University Press. pp. 181--207.
Quantum Teleportation.H. J. Kimble - 1999 - Vienna Circle Institute Yearbook 7:141-146.
Quantum Probability and the Foundations of Quantum Theory.Luigi Accardi - 1990 - In Roger Cooke & Domenico Costantini (eds.), Boston Studies in the Philosophy of Science. Springer Verlag. pp. 119-147.
Correlations, Contextuality and Quantum Logic.Allen Stairs & Jeffrey Bub - 2013 - Journal of Philosophical Logic 42 (3):483-499.


Added to PP index

Total views
1 ( #1,124,656 of 2,312,747 )

Recent downloads (6 months)
1 ( #492,511 of 2,312,747 )

How can I increase my downloads?

Monthly downloads

Sorry, there are not enough data points to plot this chart.

My notes

Sign in to use this feature