Probabilistic theories stable under teleportation

• URL: http://arxiv.org/abs/2603.21347v1
• Date: Sun, 22 Mar 2026 18:16:01 GMT
• Title: Probabilistic theories stable under teleportation
• Abstract summary: A long-standing problem in the foundations of quantum mechanics is to identify a physical principle that explains why maximal violations of Bell inequalities can not be achieved in Nature.<n>One recently proposed approach considers iterated Bell tests, where a Bell test is performed on a state that has undergone several rounds of entanglement swapping.<n>We give a classification of all general probabilistic theories whose CHSH value is stable in the above sense.
• Score: 0.17188280334580194
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A long-standing problem in the foundations of quantum mechanics is to identify a physical principle that explains why algebraically maximal violations of Bell inequalities can generally not be achieved in Nature. One recently proposed approach considers iterated Bell tests, where a Bell test is performed on a state that has undergone several rounds of entanglement swapping. Obtaining large violations in this scenario is more demanding, because it requires a theory to have both highly entangled states and highly entangled measurements. It has been conjectured that the maximal quantum mechanical Clauser-Horne-Shimony-Holt (CHSH)-value of $2\sqrt2$ might be optimal for any probabilistic theory which, like quantum mechanics, maintains its CHSH-value after an arbitrary number of rounds of entanglement swapping. However, in a previous paper, we have exhibited a first example of a probabilistic theory that can sustain a CHSH value of $4$ in this setting. In this work, further investigating this property, we give a classification of all general probabilistic theories (GPTs) whose CHSH value is stable in the above sense. The problem reduces to a representation-theoretic condition that allows for exactly seven solutions. The GPT from our previous work showed some counter-intuitive features, e.g. that the local state space had a higher dimension than seemed necessary to realize CHSH tests. The classification shows that this is necessarily so. Along the way, we generalize the concept of self-testing to GPTs.

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