TY - JOUR

T1 - Complete Hierarchy for High-Dimensional Steering Certification

AU - De Gois, Carlos

AU - Plávala, Martin

AU - Schwonnek, René

AU - Gühne, Otfried

N1 - Funding Information: Many thanks to T. Cope, H. C. Nguyen, and R. Uola for useful discussions, and to the developers and maintainers of J ulia , scs , and J u MP . We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Projects No. 447948357 and No. 440958198), the Sino-German Center for Research Promotion (Project M-0294), the ERC (Consolidator Grant 683107/TempoQ), and the German Ministry of Education and Research (Project QuKuK, BMBF Grant No. 16KIS1618K). C. G. acknowledges support from the House of Young Talents of the University of Siegen. M. P. acknowledges support from the Alexander von Humboldt Foundation. R. S. acknowledges financial support by the BMBF project ATIQ and the Quantum Valley Lower Saxony. The omni cluster of the University of Siegen was used for the computations.

PY - 2023/7/7

Y1 - 2023/7/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85164539709&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2212.12544

DO - 10.48550/arXiv.2212.12544

M3 - Article

AN - SCOPUS:85164539709

VL - 131

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

IS - 1

M1 - 010201

ER -