Equivalence between simulability of high-dimensional measurements and high-dimensional steering

Understand

The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements.

• Recently, it was shown that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering.
• While this naturally connects to the dimensionality of entanglement (Schmidt number), we show that this effect also directly connects to a notion of dimension for measurement incompatibility.
• More generally, we present a general connection between the concepts of steering and measurement incompatibility, when quantified in terms of dimension.