Quantum communication and Bell nonlocality require infinite classical communication to simulate
Abstract
A quantum system of any fixed dimension can be prepared in a continuum of states, yet it cannot be used to transmit an unlimited amount of classical information. Similarly, the correlations observed between measurement outcomes on separate parts of a shared quantum system can be stronger than classical correlations, but they cannot transmit information. These fundamental limitations suggest that the statistics observed from quantum communication and quantum correlations may admit a simulation using a finite amount of classical communication. This expectation is confirmed in the smallest nontrivial quantum dimension, with two classical bits being necessary and sufficient to exactly simulate qubit communication and all correlations between qubits. Despite significant efforts during the previous decades, this remained the only solved case. Here we resolve both problems for every quantum dimension. The solution reveals an unexpected qualitative transition starting at dimension four: no finite amount of classical communication can exactly simulate ququart communication nor all quantum correlations of two entangled ququarts, even with unlimited shared randomness. One might have expected this transition, if it existed, to appear already for qutrits. Instead, we construct an explicit protocol that exactly simulates qutrit communication using $357$ classical bits, and consequently, all correlations of two entangled qutrits.
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BibTeX
@misc{gois2026quantum,
title = {{Quantum communication and Bell nonlocality require infinite classical communication to simulate}},
author = {Carlos de Gois and Thyago S. R. Santos and Carlos Vieira},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04182},
eprint = {2609.04182},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04182},
}
RIS
TY - UNPB
TI - Quantum communication and Bell nonlocality require infinite classical communication to simulate
AU - Carlos de Gois
AU - Thyago S. R. Santos
AU - Carlos Vieira
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04182
UR - https://arxiv.org/abs/2609.04182
AB - A quantum system of any fixed dimension can be prepared in a continuum of states, yet it cannot be used to transmit an unlimited amount of classical information. Similarly, the correlations observed between measurement outcomes on separate parts of a shared quantum system can be stronger than classical correlations, but they cannot transmit information. These fundamental limitations suggest that the statistics observed from quantum communication and quantum correlations may admit a simulation using a finite amount of classical communication. This expectation is confirmed in the smallest nontrivial quantum dimension, with two classical bits being necessary and sufficient to exactly simulate qubit communication and all correlations between qubits. Despite significant efforts during the previous decades, this remained the only solved case. Here we resolve both problems for every quantum dimension. The solution reveals an unexpected qualitative transition starting at dimension four: no finite amount of classical communication can exactly simulate ququart communication nor all quantum correlations of two entangled ququarts, even with unlimited shared randomness. One might have expected this transition, if it existed, to appear already for qutrits. Instead, we construct an explicit protocol that exactly simulates qutrit communication using $357$ classical bits, and consequently, all correlations of two entangled qutrits.
ER -