Coherent Control of Channel Dilations Activate Temporal Bell Nonclassicality

The temporal Clauser-Horne-Shimony-Holt (CHSH) inequality witnesses the nonclassicality of temporal correlations, but its violation is generally degraded by environmental noise. Here, we show that violation of the temporal CHSH inequality can be revived through coherent control of noisy quantum evolutions. We compare two physically distinct implementations: coherent control of noisy evolutions induced by interaction of the system with independent environments, and coherent control of two physically distinct, unitarily equivalent Stinespring dilations of the same noisy channel. Although these constructions generate identical deterministic system dynamics, they induce distinctly different post-selected evolutions. With a focus on the amplitude damping channel (ADC), we show that coherent control of equivalent dilations extend the range of temporal CHSH inequality violation well beyond both the incoherently controlled, or deterministic, scenario and what is achievable with independent environments. Under setting-independent post-selection of the coherent control implementation, the resulting violation further certifies that the channel is not strongly CHSH nonlocality-breaking. Our results identify the choice of Stinespring dilation as an operationally relevant resource in coherently controlled tests of temporal quantum correlations.