Paper

{
  "raw_xml": "<entry>\n    <id>http://arxiv.org/abs/2603.21347v1</id>\n    <title>Probabilistic theories stable under teleportation</title>\n    <updated>2026-03-22T18:16:01Z</updated>\n    <link href='https://arxiv.org/abs/2603.21347v1' rel='alternate' type='text/html'/>\n    <link href='https://arxiv.org/pdf/2603.21347v1' rel='related' title='pdf' type='application/pdf'/>\n    <summary>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.</summary>\n    <category scheme='http://arxiv.org/schemas/atom' term='quant-ph'/>\n    <published>2026-03-22T18:16:01Z</published>\n    <arxiv:comment>18 pages, 7 figures</arxiv:comment>\n    <arxiv:primary_category term='quant-ph'/>\n    <author>\n      <name>Lionel J. Dmello</name>\n    </author>\n    <author>\n      <name>David Gross</name>\n    </author>\n  </entry>"
}