Experimental Demonstration of Robust Quantum Steering

We analyze and experimentally demonstrate quantum steering using criteria based on generalized entropies and criteria with minimal assumptions based on the so-called dimension-bounded steering. Further, we investigate and compare their robustness against experimental imperfections such as misalignment in the shared measurement reference frame. While entropy based criteria are robust against imperfections in state preparation, we demonstrate an advantage in dimension-bounded steering in the presence of measurement imprecision. As steering with such minimal assumptions is easier to reach than fully nonlocal correlations, and as our setting requires very little trust in the measurement devices, the results provide a candidate for the costly Bell tests while remaining highly device independent.

Figure 1

The Poincaré (Bloch) spheres (a)–(c) contain vectors showing one of the eigenstates of the two relevant directions (blue and red) in the experiments we performed. (a) Alice’s directions, in the case where Alice and Bob share a reference direction. We test the robustness of our inequalities to rotations in the plane (yellow), as the blue and red settings are rotated through 90° in steps (blue and red dots). $\mathrm{\Phi }=0°$ denotes the fact that the plane is not tilted with respect to Bob. (b) Alice’s directions for $m=2$ are tilted by $\mathrm{\Phi }=30°$. (c) Bob uses the same two measurement directions in each experiment. (d) The experiment consisted of entangled photon pair generation at 820 nm via SPDC in a Sagnac interferometer constructed of a polarizing beam splitter (PBS), two mirrors (M), a dual-coated half-wave plate (HWP), and a periodically poled KTP (ppKTP) crystal. Different measurement settings are performed by rotating HWP and quarter-wave plates (QWP) relative to the PBS. Long pass (LP) filters and an additional bandpass filter in Bob’s line, remove 410 nm pump photons copropagating with the 820 nm photons before photons are coupled into single-mode fibers and detected by single photon counting modules and counting electronics.

Figure 2

Steering parameters for experiments with $m=2$ measurement directions. Renyi (black square), Shannon (blue circle), Tsallis (red diamond) entropy criteria and dimension bounded steering parameter (yellow triangle) as a function of the rotation angle $\alpha$ (degrees) in Alice’s measurement plane. Angle $\mathrm{\Phi }$ denotes the angle of tilt between Alice’s and Bob’s measurement plane. Error bars are too small to be seen.