Geometric and Exotic Contextuality in Quantum Reality

Arkady Plotnitsky

Sally Shrapnel, Fabio Costa

Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot be explained by non-contextual ontological models, where physical properties are assumed to exist prior to and independently of the act of measurement. However, all such contextuality proofs assume a traditional notion of causal structure, where causal influence flows from past to future according to ordinary dynamical laws. This leaves open the question of whether the apparent contextuality of quantum mechanics is simply the signature of some exotic causal structure, where the future might affect the past or distant systems might get correlated due to non-local constraints. Here we show that quantum predictions require a deeper form of contextuality: even allowing for arbitrary causal structure, no model can explain quantum correlations from non-contextual ontological properties of the world, be they initial states, dynamical laws, or global constraints.

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'.

Jincheng Zhang

Quantum mechanics fundamentally challenges classical intuitions regarding reality and measurement, most notably through contextuality theorems such as Kochen-Specker and Bell-type inequalities. Traditional formulations treat measurement contexts as discrete sets of compatible observables or operational setups without a native, continuous geometric topology. In this paper, we introduce the framework of Quantum Measurement Context Curvature (QMCC), proposing that sequential, non-commutative measurements and environments naturally induce an irreducible geometric structure known as context curvature. By defining measurement contexts as ordered tuples C = (M_1, M_2, ..., M_n) and constructing non-commutative loops in context space, we quantify the path-dependence of quantum transition probabilities. We formalize the context curvature R_C as a sum over loops involving conditional probability discrepancies between alternative measurement orderings. This geometric perspective transcends standard operational descriptions, establishing a formal bridge between non-commutative algebraic structures of quantum mechanics and differential geometry, with potential applications in foundational quantum mechanics and advanced quantum information processing.

Mary Bell, Shan Gao