Complete hierarchy for high-dimensional steering certification

TL;DR

This paper introduces a comprehensive hierarchy of semidefinite programs for certifying and quantifying high-dimensional quantum steering, providing stronger bounds and practical methods for experimental verification of high-dimensional entanglement.

Contribution

It presents necessary and sufficient conditions for entanglement dimension certification in high-dimensional steering using a hierarchy of semidefinite programs, including a robustness measure.

Findings

Stronger bounds on noise robustness for certification

Effective characterization of entanglement dimensionality with maximally entangled states

Practical certification method demonstrated with experimental scenarios

Abstract

High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.