The axiom of choice and the no-signalling principle

Autor(en)

Ämin Baumeler, Borivoje Dakić, Flavio Del Santo

Abstrakt

We show that the axiom of choice, a basic yet controversial postulate of set theory, together with one of the pillars of our best physical theories, namely the no-signalling principle, may point to a limitation in modelling physical problems using standard mathematics. While it is well known that probabilistic no-signalling resources (such as quantum non-locality) are stronger than deterministic ones, we show - by invoking the axiom of choice - the opposite: functional (deterministic) no-signalling resources can be stronger than probabilistic ones (e.g. stronger than quantum entanglement or non-locality in general). To prove this, we devise a Bell-like game that shows a systematic advantage of functional no-signalling with respect to any probabilistic no-signalling resource.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Università della Svizzera Italiana, Facoltà Indipendente di Gandria, Österreichische Akademie der Wissenschaften (ÖAW), Universität Genf

Journal

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Band

481

Anzahl der Seiten

9

ISSN

1364-5021

DOI

https://doi.org/10.48550/arXiv.2206.08467

Publikationsdatum

07-2025

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik

Schlagwörter

ASJC Scopus Sachgebiete

Allgemeine Mathematik, Allgemeiner Maschinenbau, Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/d1a787cf-cf51-4631-bf46-9bde31c99c05