量子通信和贝尔非定域性需要无限的经典通信才能模拟

中文摘要 AI 辅助

任意固定维度的量子系统可制备出连续统的态，却无法用于传输无限量的经典信息；同理，共享量子系统不同部分测量结果间的关联可强于经典关联，但无法传输信息。这些基本限制表明，量子通信与量子关联的观测统计量或许可利用有限量的经典通信模拟。该预期在最小非平凡量子维度（即2）中得到证实：2个经典比特是精确模拟量子比特通信及所有量子比特间关联的必要且充分条件。尽管过去几十年付出了巨大努力，这仍是唯一已解决的情况。本文针对所有量子维度解决了这两个问题，该解决方案揭示了一个从维度4开始的意外定性转变：即使存在无限共享随机性，也没有有限量的经典通信能精确模拟量子四元组（ququart）通信或两个纠缠量子四元组的所有量子关联。人们原本以为，若存在这种转变，它应已出现在量子三重组（qutrit）的情况中。相反，我们构建了一个明确协议，利用357个经典比特精确模拟量子三重组通信，进而精确模拟两个纠缠量子三重组的所有关联。

英文摘要

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.

发表机构

• CPHT, LIX, CNRS, Inria, École polytechnique, Institut Polytechnique de Paris（巴黎高等师范学院、巴黎综合理工学院）
• Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas（坎皮纳斯州立大学）
• Sorbonne Université, CNRS, LIP6（索邦大学）

机构由 AI 辅助整理，请以论文原文为准。