PreprintarXiv licencearXiv
On the signaling dimension of the cross-polytope
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.
Related
- A 5/8 Lower Bound on the Banach--Mazur Distance to the Cross-Polytope
- Gaussian polytopes with large Banach-Mazur distance to the cross-polytope
- The point-cross dimension
- On the second smallest ideal right-angled hyperbolic four-polytope
- On the magic positivity of the Ehrhart polynomials of dilated base polytope of minimal matroid
BibTeX
@misc{bencze2026signaling,
title = {{On the signaling dimension of the cross-polytope}},
author = {Tamás Bencze and Péter E. Frenkel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05924},
eprint = {2610.05924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05924},
}
RIS
TY - UNPB
TI - On the signaling dimension of the cross-polytope
AU - Tamás Bencze
AU - Péter E. Frenkel
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.05924
UR - https://arxiv.org/abs/2610.05924
AB - 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.
ER -