Reality, Contextuality, and Probability in Quantum Theory and Beyond

Ehtibar N. Dzhafarov

Michel R. P. Planat

Arkady Plotnitsky

This article brings together reality, complementarity and contextuality in quantum theory. It clarifies Bohr's concept of complementarity by considering the non-realist epistemology and the corresponding interpretations of quantum mechanics, based in the concept of 'reality without realism'. Finally, as its main novel contribution, it establishes the connections between complementarity and contextuality. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

Claudio Garola

Sally Shrapnel, Fabio Costa, Gerard J Milburn

Despite the tremendous empirical success of quantum theory there is still widespread disagreement about what it can tell us about the nature of the world. A central question is whether the theory is about our knowledge of reality, or a direct statement about reality itself. Current interpretations of quantum theory, regardless of their stance on this question, regard the Born rule as fundamental and add an independent state update (or 'collapse') rule to describe how quantum states change upon measurement. In this paper we present an alternative perspective and derive a unified probability rule that subsumes both the Born rule and the collapse rule. We show that this more fundamental probability rule can provide a rigorous foundation for informational, or 'knowledge-based', interpretations of quantum theory. Our result requires an assumption of instrument non-contextuality, a key notion that generalises previous approaches to non-contextuality. Therefore, the framework also permits one to consider non-contextuality in scenarios with arbitrary causal structure.

J. Acácio de Barros, Federico Holik, Décio Krause

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent.Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities.In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability.In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same.We will discuss how the consequences of this move may help us understand quantum contextuality.