Comparing Quantum and Classical Finite State Generators

Bell-CHSH-like inequalities have been very successful in benchmarking spatial quantum correlations. However, as this paper illustrates, they are not necessarily sufficient for benchmarking temporal quantum correlations. To illustrate this, we parametrise classical and quantum stochastic finite state generators based on a single bit and a single qubit, respectively, and compare the temporal correlations of their output sequences using a Bell-CHSH-like inequality. We find that for sequential measurements by two observers, classical machines can exceed the Tsirelson bound of 22. To present at least one example in which quantum machines outperform their classical counterparts and maintain correlations for longer, we consider general scrambling operations between consecutive measurements. Our analysis shines new light on the fundamental differences between quantum and classical finite state generators and can potentially be used to identify novel resources for quantum technology applications.