Continuous-Variable Nonlocality and Contextuality

Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been discrete-variable scenarios, where observables take values discrete and usually finite sets. Practically, on the other hand, continuous-variable scenarios offer some of most promising candidates implementing computations protocols. Here we set out framework treating contextuality scenarios. shown Fine–Abramsky–Brandenburger theorem extends this setting, an important consequence which Bell nonlocality viewed as special case contextuality, case. The contextual fraction, quantifiable measure bears precise inequality violations advantages, also defined setting. non-increasing monotone with respect classical operations include binning discretise data. Finally, consider how fraction formulated infinite linear program. Through Lasserre relaxations, are able express program hierarchy semi-definite programs allow calculate increasing accuracy.