Classically high-dimensional correlation: simulation of high-dimensional entanglement

Classical correlation, akin to the entanglement of quantum states, has been proven to bear a great promise in classical and quantum systems, such as enhancing measurement precision and characterizing quantum channels. Despite numerous successful applications of such correlation, it is strictly limited to two orthogonal bases and fails to further extend its dimensionality in practice. Here, we report a classically high-dimensional correlation, which is mathematically equivalent to its quantum counterparts and can be used to simulate the violations of the high-dimensional Bell inequalities. Moreover, we also show theoretically that quantum channels with high-dimensional quantum states can be characterized robustly using our scheme when a one-sided channel is perturbed by a turbulent atmosphere. This means that our results not only provide new physical insights into the notion of classical correlation, but also show potential applications in high-dimensional quantum information processing.