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
(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-signaling with respect to any
probabilistic no-signaling resource.
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