Year: 2026
Type: preprint
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 logarithmic lower and upper bounds for the signaling dimensions of higher dimensional cross-polytopes, pinning down the value up to an additive gap of 2. The lower bound shows that the signaling dimension goes to infinity, in contrast to the case of balls and hypercubes.
Source: arXiv (Cornell University)
Authors: Bencze, Tamás, Frenkel, Péter E.
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G2637195304, G737807411, G8467544433
OpenAlex ID: W7220704083