Abstract

We report on our results investigating bounds on temporal correlations achievable by classical and quantum systems under various discrete-time scenarios, with the assumption of a finite memory resource. This memory constraint imposes fundamental limitations on realizable correlations, which may be exploited to construct dimensional witnesses. In this seminar, I will report on our investigation on temporal correlations in the simplest measurement scenario, i.e., that of a physical system on which the same measurement is performed at different times, producing a sequence of dichotomic outcomes. We characterize the minimum memory requirements for sequences to be obtained deterministically, and numerically investigate the probabilistic behavior below this memory threshold, in both classical and quantum scenarios. A particular class of sequences is found to offer an upper-bound for all other sequences, which suggests a nontrivial universal upper-bound of 1/e for the classical probability of realization of any sequence below the deterministic memory threshold. We further present evidence that no such nontrivial bound exists in the quantum case. Additional comments on applications will also be discussed, if time allows.

Link: https://quantum-journal.org/papers/q-2022-01-18-623/