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This research resolves the long-standing problem of simulating quantum communication across all dimensions, revealing a sharp transition where infinite classical resources become necessary for systems of dimension four or higher. The study establishes explicit protocols for lower dimensions, such as using 357 classical bits to perfectly simulate qutrit correlations, while proving that ququarts and larger systems fundamentally cannot be simulated with finite classical means even with unlimited shared randomness. These findings deepen our understanding of the boundary between quantum and classical information processing limits.
Quantum communication and Bell nonlocality require infinite classical communication to simulate
arXiv:2609.04182v1 Announce Type: new 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.
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.
arXiv:2609.04182 [quant-ph]
(or arXiv:2609.04182v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.04182 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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