The Axiom of Choice and the No-Signaling Principle

• URL: http://arxiv.org/abs/2206.08467v2
• Date: Thu, 7 Jul 2022 18:35:04 GMT
• Title: The Axiom of Choice and the No-Signaling Principle
• Authors: \"Amin Baumeler, Borivoje Daki\'c, and Flavio Del Santo
• Abstract summary: We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories. We show-by invoking the axiom of choice-the opposite: Functional (deterministic) no-signaling resources can be stronger than probabilistic ones.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the axiom of choice, a basic yet controversial postulate of set theory, leads to revise the standard understanding of one of the pillars of our best physical theories, namely the no-signaling principle. While it is well known that probabilistic no-signaling resources (such as quantum non-locality) are stronger than deterministic ones, we show-by invoking the axiom of choice-the opposite: Functional (deterministic) no-signaling resources can be stronger than probabilistic ones. To prove this, we devise a Bell-like game that shows a systematic advantage of functional no-signaling with respect to any probabilistic no-signaling resource.

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