Experimental High-Dimensional Einstein-Podolsky-Rosen Steering

Steering nonlocality is the fundamental property of quantum mechanics, which has been widely demonstrated in some systems with qubits. Recently, theoretical works have shown that the high-dimensional (HD) steering effect exhibits novel and important features, such as noise suppression, which appear promising for potential application in quantum information processing (QIP). However, experimental observation of these HD properties remains a great challenge to date. In this work, we demonstrate the HD steering effect by encoding with orbital angular momentum photons for the first time. More importantly, we have quantitatively certified the noise-suppression phenomenon in the HD steering effect by introducing a tunable isotropic noise. We believe our results represent a significant advance of the nonlocal steering study and have direct benefits for QIP applications with superior capacity and reliability.

Figure 1

Experimental schematic of HD steering certification. Pumper: Coherent Chameleon (centered at 800 nm). Second harmonic generation (SHG) (300 mw at 400 nm). 3 mm-long non-collinear type-I nonlinear BBO crystal (BBO). Half-wave plate (HWP). Spatial light modulator (SLM) (model: Holoeye—LETO). Collector: photon to fiber collector embedded with narrow bandwidth filter (800 nm, $\pm 5\mathrm{nm}$). Single mode fiber (SMF) (diameter: $5\mu \mathrm{m}$).

Figure 2

Experimental results of coincidence measurement. (a) Experimental coincidence counts of jointly measuring state ${|{\ell }_{\mathrm{i}}⟩}_A{|{\ell }_{\mathrm{j}}⟩}_B({\ell }_{\mathrm{i}},{\ell }_{\mathrm{j}}=-2,\dots ,+2)$. (b) Experimental values of the steering parameter $S_{\mathrm{\Phi }}^{(\mathrm{EPR})}$ versus different system dimension. The coincidence time of our experiment is 10 s and errors were estimated assuming Poisson statistics. The detailed standard derivation and error analysis are provided in Sec. II of the Supplemental Material [41].

Figure 3

Animation configuration of generating the isotropic state. Random number generator (RNG). For every specific $d$ and $p$, we construct one animation with which we implement the measurement.

Figure 4

Experimental results of steering certification with tunable isotropic noise. (a)–(d) Steering parameter $S_{\mathrm{\Phi }}^{(\mathrm{EPR})}$ for different percentage of isotropic noise in different dimensions. (e) Actual $P_{\min }$ for dimension 2 to 5. Errors were estimated assuming Poisson statistics. The detailed standard derivation is provided in Sec. II of the Supplemental Material [41].