Bernstein’s Socks, Polynomial-Time Provable Coherence and Entanglement

Alessio Benavoli, Alessandro Facchini, Marco Zaffalon
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:23-31, 2019.

Abstract

We recently introduced a bounded rationality approach for the theory of desirable gambles. It is based on the unique requirement that being nonnegative for a gamble has to be defined so that it can be provable in polynomial time. In this paper we continue to investigate properties of this class of models. In particular we verify that the space of Bernstein polynomials in which nonnegativity is specified by the Krivine-Vasilescu certificate is yet another instance of this theory. As a consequence, we show how it is possible to construct in it a thought experiment uncovering entanglement with classical (hence non quantum) coins.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-benavoli19a, title = {Bernstein’s Socks, Polynomial-Time Provable Coherence and Entanglement}, author = {Benavoli, Alessio and Facchini, Alessandro and Zaffalon, Marco}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {23--31}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/benavoli19a/benavoli19a.pdf}, url = {https://proceedings.mlr.press/v103/benavoli19a.html}, abstract = {We recently introduced a bounded rationality approach for the theory of desirable gambles. It is based on the unique requirement that being nonnegative for a gamble has to be defined so that it can be provable in polynomial time. In this paper we continue to investigate properties of this class of models. In particular we verify that the space of Bernstein polynomials in which nonnegativity is specified by the Krivine-Vasilescu certificate is yet another instance of this theory. As a consequence, we show how it is possible to construct in it a thought experiment uncovering entanglement with classical (hence non quantum) coins.} }
Endnote
%0 Conference Paper %T Bernstein’s Socks, Polynomial-Time Provable Coherence and Entanglement %A Alessio Benavoli %A Alessandro Facchini %A Marco Zaffalon %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-benavoli19a %I PMLR %P 23--31 %U https://proceedings.mlr.press/v103/benavoli19a.html %V 103 %X We recently introduced a bounded rationality approach for the theory of desirable gambles. It is based on the unique requirement that being nonnegative for a gamble has to be defined so that it can be provable in polynomial time. In this paper we continue to investigate properties of this class of models. In particular we verify that the space of Bernstein polynomials in which nonnegativity is specified by the Krivine-Vasilescu certificate is yet another instance of this theory. As a consequence, we show how it is possible to construct in it a thought experiment uncovering entanglement with classical (hence non quantum) coins.
APA
Benavoli, A., Facchini, A. & Zaffalon, M.. (2019). Bernstein’s Socks, Polynomial-Time Provable Coherence and Entanglement. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:23-31 Available from https://proceedings.mlr.press/v103/benavoli19a.html.

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