Advantage of Hardy's Nonlocal Correlation in Reverse Zero-Error Channel Coding

Hardy's argument constitutes an elegant proof of quantum nonlocality as established by the seminal Bell's theorem. In this work, we report an exotic application of Hardy's nonlocal correlations. We devise a simple communication task and show that the expected payoff of the task cannot be positive whenever only 1-cbit communication is allowed from the sender to the receiver, who otherwise can share an unlimited amount of classical correlation. Interestingly, the same classical channel can ensure a positive payoff when assisted with correlations exhibiting Hardy's nonlocality. As it turns out, among all the 2-input-2-output no-signaling correlations, only Hardy's correlation can ensure a positive payoff when assisted to 1-cbit channel. This further prompts us to show that in the correlation assisted reverse zero-error channel coding scenario, where the aim is to simulate a noisy channel exactly by a noiseless one in assistance with correlations, assistance of non-maximally pure entangled states -- even with vanishingly zero amount of entanglement -- could be preferable over the maximal one.