Generic Contextuality

Wei Li, Zhou Min-xuan, Yun‐Hao Shi +3 more

We reveal that the entropic uncertainty relation with a quantum memory is able to intrinsically connect local generic contextuality addressed in the pioneering work by Spekkens and nonlocal quantum resources such as entanglement and Bell nonlocality. Based on the constructed optimal set for any given single-qubit state, we prove rigorously a faithful criterion to witness the generic contextuality in the scenario of local quantum state preparation. Furthermore, within the framework of quantum resource distribution, it is proved that there exist quantitative trade-off relations between local preparation contextuality and bipartite entanglement or Bell nonlocality in a shared quantum system, which are captured by two inequalities where the local and nonlocal quantum resources can coexist. The faithful criterion and quantitative inequalities are all experimentally testable, which are verified through two independent well-designed experiments on the Quafu quantum cloud platform.

Costantino Budroni, Adán Cabello, Otfried Gühne +2 more

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here, compatible measurements are those that can be performed simultaneously or in any order without disturbance. This conflict is generically called quantum contextuality. In this article, we present an introduction to this subject and its current status. We review several proofs of the Kochen-Specker theorem and different notions of contextuality. We explain how to experimentally test some of these notions and discuss connections between contextuality and nonlocality or graph theory. Finally, we review some applications of contextuality in quantum information processing.

Marek Woszczek

Quantum contextuality and its ontological meaning are very controversial issues, and they relate to other problems concerning the foundations of quantum theory. I address this controversy and stress the fact that contextuality is a universal topological property of quantum processes, which conflicts with the basic metaphysical assumption of the definiteness of being. I discuss the consequences of this fact and argue that generic quantum potentiality as a real physical indefiniteness has nothing in common with the classical notions of possibility and counterfactuality, and that also it reverses, in a way, the classical mirror-like relation between actuality and definite possibility.

Douglas L. Hemmick, Asif M. Shakur