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Complete hierarchy for high-dimensional steering certification

Carlos de GoisMartin Pl\'avalaRen\'e SchwonnekOtfried G\"uhne
Dec 2022
摘要
High-dimensional quantum steering can be seen as a test for thedimensionality of entanglement, where the devices at one side are notcharacterized. As such, it is an important component in quantum informationalprotocols that make use of high-dimensional entanglement. Although it has beenrecently observed experimentally, the phenomenon of high-dimensional steeringis lacking a general certification procedure. We provide necessary andsufficient conditions to certify the entanglement dimension in a steeringscenario. These conditions are stated in terms of a hierarchy of semidefiniteprograms, which can also be used to quantify the phenomenon using the steeringdimension robustness. To demonstrate the practical viability of our method, wecharacterize the dimensionality of entanglement in steering scenarios preparedwith maximally entangled states measured in mutually unbiased bases. Ourmethods give significantly stronger bounds on the noise robustness necessary toexperimentally certify high-dimensional entanglement.
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