Comparing quantum and classical finite state generators

TL;DR

This paper compares quantum and classical finite state generators, showing that quantum systems can outperform classical ones in temporal correlations under certain conditions, challenging traditional benchmarking methods.

Contribution

It demonstrates that Bell-CHSH-like inequalities are insufficient for temporal quantum correlations and introduces new ways to distinguish quantum from classical processes.

Findings

Classical machines can exceed the Tsirelson bound in sequential measurements.

Quantum machines maintain correlations longer under scrambling operations.

Quantum systems outperform classical ones with time delays between measurements.

Abstract

Bell-CHSH-like inequalities have been very successful in benchmarking {\it spatial} quantum correlations. However, as this paper illustrates, they are in general not sufficient for benchmarking {\it temporal} quantum correlations. To show 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, Alice and Bob, classical machines can exceed the Tsirelson bound of $2\sqrt{2}$, due to their fundamental structure. However, when we consider a time delay between consecutive measurements, we find examples where the quantum machines outperform their classical counterparts by maintaining correlations longer under generally scrambling operations. Our result can be used to distinguish quantum from classical processes and to identify novel resources for quantum technology applications.