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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