Almost-Quantum Correlations Violate Information Causality
Abstract
Information causality (IC) posits that communicating m classical bits cannot give the receiver access to more than m bits of information about the sender's independent data. Although IC holds in quantum theory and excludes a broad class of supra-quantum correlations, its validity for the almost-quantum set has remained open. This semidefinite relaxation of the quantum set satisfies nontrivial communication complexity, no advantage for non-local computation, macroscopic locality, local orthogonality, and numerical evidence has suggested that it may also satisfy IC. Here we show that almost-quantum correlations violate IC, and do so without bound. Unlike earlier violations of IC, which rely on biased guesses, ours is driven by zero-error certificates: each is rare but never wrong, carries information linear in its probability, and vouches for many of the sender's bits at once. This establishes a sharp dichotomy: either IC is a valid physical principle that excludes these correlations, or any nonsignalling theory realizing them admits no mutual information obeying consistency, data processing and the chain rule. In the latter case, we discuss why the chain rule is the natural property to relinquish, and how this possibility relates to histories-based formulations and to locality defined relative to the state rather than presupposed in a fixed spacetime.
Related
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BibTeX
@misc{bhowmik2026almostquantum,
title = {{Almost-Quantum Correlations Violate Information Causality}},
author = {Anandamay Das Bhowmik and Manik Banik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41444},
eprint = {2610.41444},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41444},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Almost-Quantum Correlations Violate Information Causality
AU - Anandamay Das Bhowmik
AU - Manik Banik
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41444
UR - https://arxiv.org/abs/2610.41444
AB - Information causality (IC) posits that communicating m classical bits cannot give the receiver access to more than m bits of information about the sender's independent data. Although IC holds in quantum theory and excludes a broad class of supra-quantum correlations, its validity for the almost-quantum set has remained open. This semidefinite relaxation of the quantum set satisfies nontrivial communication complexity, no advantage for non-local computation, macroscopic locality, local orthogonality, and numerical evidence has suggested that it may also satisfy IC. Here we show that almost-quantum correlations violate IC, and do so without bound. Unlike earlier violations of IC, which rely on biased guesses, ours is driven by zero-error certificates: each is rare but never wrong, carries information linear in its probability, and vouches for many of the sender's bits at once. This establishes a sharp dichotomy: either IC is a valid physical principle that excludes these correlations, or any nonsignalling theory realizing them admits no mutual information obeying consistency, data processing and the chain rule. In the latter case, we discuss why the chain rule is the natural property to relinquish, and how this possibility relates to histories-based formulations and to locality defined relative to the state rather than presupposed in a fixed spacetime.
ER -