We propose a cryptography-inspired model for nonlocal correlations. Following the celebrated De Broglie-Bohm theory, we model nonlocal boxes as realistic systems with instantaneous signalling at the hidden variable level. By introducing randomness in the distribution of the hidden variable, the superluminal signalling model is made compatible with the operational no-signalling condition. As the design mimics the famous symmetric key encryption system called {\it One Time Pads} (OTP), we call this the OTP model for nonlocal boxes. We demonstrate utility of this model in several esoteric examples related to the nonclassicality of nonlocal boxes. In particular, the breakdown of communication complexity using nonlocal boxes can be better understood in this framework. Furthermore, we discuss the Van Dam protocol and show its connection to homomorphic encryption in cryptography. We also discuss possible ways of encapsulating quantum realizable nonlocal correlations within this framework and show that the principle of Information Causality imposes further constraints at the hidden variable level. Present work thus orchestrates the results in classical cryptography to improve our understanding of nonlocal correlations and welcomes further research to this connection.
翻译:我们提出了一种受密码学启发的非局域关联模型。遵循著名的德布罗意-玻姆理论,我们将非局域盒建模为在隐变量层面存在即时信号传递的实在论系统。通过在隐变量分布中引入随机性,超光速信号模型得以与操作上的无信号条件兼容。由于该设计模仿了著名的对称密钥加密系统——一次性密码本(One Time Pads,OTP),我们将其称为非局域盒的OTP模型。我们通过几个与非局域盒的非经典性相关的深奥示例,展示了该模型的实用性。特别是,利用非局域盒打破通信复杂性的现象在该框架下能得到更好的理解。此外,我们讨论了Van Dam协议,并展示了其与密码学中同态加密的联系。我们还探讨了在该框架内封装量子可实现非局域关联的可能性,并证明了信息因果性原理在隐变量层面施加了进一步的约束。因此,本工作通过整合经典密码学的研究成果,旨在加深我们对非局域关联的理解,并欢迎后续研究探索这一联系。