Original title: Quantum communication and Bell nonlocality require infinite classical communication to simulate
Carlos de Gois, Thyago S. R. Santos, Carlos Vieira · September 2026
Can normal digital bits copy the behavior of quantum systems? Quantum particles can exist in an endless variety of states, but they cannot transmit unlimited ordinary information. Particles also share links that produce strange measurement patterns without sending signals. Because of these limits, scientists wondered if standard computer messages, or classical communication, could fully recreate these quantum results. Earlier work showed that two classical bits can copy a two-level quantum system, called a qubit. In this paper, researchers tested every quantum dimension. They built a recipe using 357 classical bits to copy three-level systems, known as qutrits. However, for four-level systems, called ququarts, everything changes. The team found that no finite amount of classical communication can ever copy ququartA quantum system with four distinguishable states. behavior, even with unlimited shared random data.
Imagine trying to describe a complex piece of music using only written notes. For a simple melody, a few bars might capture it exactly. For a richer composition, you might need a full sheet music score of hundreds of notes. But for some symphonies, no matter how many notes you write, you can never perfectly convey every nuance and timing in finite words. In this paper, quantum communication is like the music, and classical bits are the written notes. For qutrits, 357 notes suffice, but for ququarts, no finite set of notes works.
This work defines the exact point where quantum systems cannot be mimicked by classical methods, affecting how we build quantum computers and design secure communication systems.
The abstract only addresses exact simulation, not approximate or practical implementations. It does not discuss noisy environments or other real-world factors.
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Quantum communication and Bell nonlocality require infinite classical communication to simulate — Carlos de Gois, Thyago S. R. Santos, Carlos Vieira
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.