Recent developments in quantum contextuality

A physical system is contextual when the result of a measurement on it might depend on which compatible observables were previously measured. We will review some recent developments on this subject:

1. Quantum nonlocality revealed by local contextuality. Two distant systems can violate a Bell inequality even though the correlations between these systems admit a local model. Nonlocality appears when testing extra correlations among successive measurements on one of the systems.

2. Macroscopic state-independent quantum contextuality. For any n-qubit system there is an inequality for the correlations among three compatible dichotomic measurements which is satisfied by any noncontextual theory, but is violated by any quantum state. The violation grows exponentially with n.

3. Memory cost of quantum contextuality. Simulating contextuality requires individual systems to have memory. We show that (log 3)/2 bits of memory per qubit are necessary and sufficient to simulate the results of some recent experiments on quantum contextuality, but one bit per qubit does not suffice if we consider an extended set of observables.