In quantum communication complexity, the classical resource requirements can be quantified through quantum statistics. In the qubit prepare-and-measure scenario, it has been shown that two classical bits are necessary and sufficient to accurately simulate arbitrary qubit states and measurements. However, this does not exclude the possibility that certain restricted families of measurements may allow for accurate one-bit classical approximations. We utilize a neural network procedure to demonstrate that a single bit can achieve high average accuracy for specific measurement families. Our performance analysis reveals that symmetric measurements with uniformly weighted elements, such as those forming regular polyhedra, are particularly suitable for this restricted communication. By analyzing the patterns learned by the neural network, we derive an analytical protocol that is extremely accurate for finite informationally complete symmetric configurations and becomes exact in the limit of continuous isotropic measurement.
Blogger's Review: This paper innovatively showcases the potential of using single bits for efficient communication in quantum measurements through a neural network approach. It offers a significant new perspective and tools for quantum information theory, particularly with promising applications under specific symmetric configurations.