Hidden nonmacrorealism: reviving the Leggett-Garg inequality with stochastic operations

Abstract

The Leggett-Garg inequality (LGI) distinguishes nonmacrorealistic channels from macrorealistic ones by constraining the experimental outcomes of the underlying system. In this work, we propose a class of channels which, initially, cannot violate the LGI (in the form of the temporal Bell inequality) but can violate it after the application of stochastic pre- and post- operations (SPPOs). As a proof-of-principle experiment, we demonstrate the stochastic pre- and post- operations in an amplitude-damping channel with photonic qubits. We denote the above phenomenon as hidden nonmacrorealistic channels. We also discuss the relationship between this hidden nonmacrorealistic channels (in terms of the temporal Clauser-Horne-Shimony-Holt (CHSH) inequality) and the strongly nonlocality-breaking channel, which breaks the hidden spatial CHSH nonlocality for arbitrary states. In general, if the channel satisfies hidden nonmacrorealism, it is not a strongly CHSH nonlocality-breaking channel.