Robust genuine high-dimensional steering with many measurements

TL;DR

This paper develops universal bounds on incompatibility robustness for high-dimensional quantum steering with multiple measurements, enhancing noise resistance and enabling better dimension certification in quantum experiments.

Contribution

It introduces a method to certify high-dimensional quantum steering with more than two measurements, improving noise resistance and overcoming previous limitations.

Findings

Bounds are loose but still improve noise resistance.

Method enables dimension certification with multiple measurements.

Applicable to high-dimensional quantum communication experiments.

Abstract

Quantum systems of high dimensions are attracting a lot of attention because they feature interesting properties when it comes to observing entanglement or other forms of correlations. In particular, their improved resistance to noise is favourable for experiments in quantum communication or quantum cryptography. However, witnessing this high-dimensional nature remains challenging, especially when the assumptions on the parties involved are weak, typically when one of them is considered as a black box. In this context, the concept of genuine high-dimensional steering has been recently introduced and experimentally demonstrated [Phys. Rev. Lett. 126, 200404 (2021)]; it allows for a one-sided device-independent certification of the dimension of a bipartite shared state by only using two measurements. Here I overcome this limitation by developing, for more than two measurements, universal bounds on the incompatibility robustness, turned into meaningful dimension certificates. Interestingly, even though the resulting bounds are quite loose, they still often offer an increased resistance to noise and could then be advantageously employed in experiments.