Ravi Kunjwal

The fact that quantum theory radically departs from 'classical lines of thought' is a critical driver for its applications in quantum information and computation. A famous example of this radical departure—this nonclassicality—is entanglement. Bell's theorem shows that shared entanglement can be used to generate correlations between non-communicating parties in ways that are impossible to do without communication if one only had access to classical shared randomness. In their very formulation, both entanglement and Bell's theorem are composite notions of nonclassicality, i.e., they require at least two parties to be meaningful. Another key notion of nonclassicality is contextuality that follows from the Kochen-Specker theorem: this notion is applicable to single systems. I will present some recent results on the interplay between contextuality and entanglement in composite systems and their consequences for our understanding of restricted models of multiqubit quantum computation with state injection that have been previously proposed. Based on V.J. Wright and R. Kunjwal, Quantum 7, 900 (2023).

We consider quantum realizations of extremal correlations in arbitrary contextuality scenarios and prove that, for all such scenarios, no extremal indeterministic correlation can be achieved using projective quantum measurements, i.e., there exists no quantum state and no set of projective measurements, for any contextuality scenario, that can achieve such correlations. This no-go result follows as a corollary of a more general no-go theorem that holds when POVMs are taken into account. This general no-go theorem entails that no non-trivial quantum realization of an extremal indeterministic correlation exists, i.e., any "quantum" realization must be simulable by classical randomness.