Signaling between time steps does not allow for nonlocality beyond hidden nonlocality

TL;DR

This paper demonstrates that signaling between different time steps does not enable nonlocal correlations beyond hidden nonlocality, establishing limits on temporal quantum correlations under no-signaling constraints.

Contribution

The work characterizes the local polytope in sequential measurement scenarios and proves no advantage of longer sequences for states with hidden nonlocality.

Findings

States with only local statistics after local filtering remain local in sequential scenarios.

The extreme points of the no-signaling polytope are determined and characterized.

No nonlocality beyond hidden nonlocality exists in the considered temporal scenario.

Abstract

Hidden nonlocality is the phenomenon that entangled states can be local in the standard Bell scenario but display nonlocality after local filtering. However, there exist entangled states for which all measurement statistics can be described via a local hidden variable model even after local filtering. In this work we consider the scenario that measurement outcomes and settings of Alice can influence measurements of Bob in subsequent time steps (and vice versa), however, there is no signaling among them for measurements at the same time step. We show that in this scenario states that only display local statistics after local filtering remain local even when considering the complete statistics of arbitrary sequences and therefore no advantage can be gained by performing longer sequences in this scenario. We first determine the extreme points of the polytope defined by the no-signaling conditions within the same time step and the arrow-of-time constraints. Based on these results we introduce a notion of locality and provide a complete representation of the corresponding local polytope in terms of inequalities in the simplest scenario. These results imply that in the scenario considered here there is no nonlocality beyond hidden nonlocality. We further propose a device-dependent Schmidt number witness and we compare our finding to known local models in the sequential scenario.