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arXiv · 2610.05924

On the signaling dimension of the cross-polytope

Tamás Bencze·Péter E. \ Frenkel
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Abstract

In the general probabilistic model of information theory, the signaling dimension of a given communication protocol (or, equivalently, of its state space) is the smallest possible complexity of a classical communication protocol capable of perfectly simulating the given one in terms of input-output correlations. The signaling dimensions of three-, four-, and five-dimensional cross-polytopes have been known to be 3. We give an upper and a lower bound for signaling dimensions of higher dimensional cross-polytopes.

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Tamás Bencze, Péter E. \ Frenkel. 2026-10-05. On the signaling dimension of the cross-polytope. https://arxiv.org/abs/2610.05924

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