Joint Measurability and Temporal Steering

TL;DR

This paper establishes a fundamental link between measurement incompatibility and temporal steering, showing that incompatible measurements are precisely those that demonstrate temporal steering, extending previous spatial steering results.

Contribution

It proves the temporal analog of the relation between measurement incompatibility and steering, connecting measurement incompatibility directly to temporal steering.

Findings

Incompatible measurements are equivalent to exhibiting temporal steering.

Extends the known relation from spatial to temporal quantum correlations.

Provides a theoretical foundation for understanding measurement incompatibility in temporal scenarios.

Abstract

Quintino et. al. (Phys. Rev. Lett. 113, 160402 (2014)) and Uola et. al. (Phys. Rev. Lett. 113, 160403 (2014)) have recently established an intrinsic relation between non-joint measurability and Einstein-Podolsky- Rosen steering. They showed that a set of measurements is incompatible (i.e., not jointly measurable) if and only if it can be used for the demonstration of steering. In this paper, we prove the temporal analog of this result viz., a set of measurements are incompatible if and only if it exhibits temporal steering.