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

• URL: http://arxiv.org/abs/2207.04080v1
• Date: Fri, 8 Jul 2022 18:11:53 GMT
• Title: Equivalence between simulability of high-dimensional measurements and high-dimensional steering
• Authors: Benjamin D.M. Jones, Roope Uola, Thomas Cope, Marie Ioannou, S\'ebastien Designolle, Pavel Sekatski and Nicolas Brunner
• Abstract summary: The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. We show that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. From this connection, we propose a novel twist on the problem of simulating quantum correlations. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement. Finally, we derive criteria for testing the dimension of measurement incompatibility, and discuss the extension of these ideas to quantum channels.

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