Non-adaptive measurement-based quantum computation and multi-party Bell inequalities

Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tasks, such as measurement-based quantum computation (MQC). In MQC, universal quantum computation can be achieved via adaptive measurements on a suitable entangled resource state. In this paper, we look at a version of MQC in which we remove the adaptivity of measurements and aim to understand what computational abilities remain in the resource. We show that there are explicit connections between this model of computation and the question of non-classicality in quantum correlations. We demonstrate this by focusing on deterministic computation of Boolean functions, in which natural generalizations of the Greenberger–Horne–Zeilinger paradox emerge; we then explore probabilistic computation via, which multipartite Bell inequalities can be defined. We use this correspondence to define families of multi-party Bell inequalities, which we show to have a number of interesting contrasting properties.