Experimental certification of the steering criterion based on a general entropic uncertainty relation

Quantum steering describes a phenomenon whereby one system can immediately influence another via local measurements. It can be detected by violating the powerful and useful steering criterion based on a general entropic uncertainty relation. This criterion can be straightforwardly evaluated by using probability distributions from a finite set of measurements. Herein, we experimentally verify the steering criterion by means of the two-photon Werner-like states and three Pauli measurements. The results indicate that quantum steering can be captured by the criterion in a convenient way. In particular, there is no need to perform the usual quantum state tomography in the experiment, which greatly reduces experimental resources. Moreover, we demonstrate that the criterion is stronger than the linear one for detecting quantum steering of the Werner-like states.

Figure 1

Experimental setup is constructed by three modules: (a) state preparation module, (b) dephase component, and (c) tomography module. In the module (a), two-photon states $\left|{\varphi }_{AB}\right.〉=cos2\theta \left|HH\right.〉+sin2\theta \left|VV\right.〉$ are prepared by the procession of a spontaneous parametric downconversion. In module (b), three $\mathrm{YV}{\mathrm{O}}_4$ crystals and a HWP with $22.5^{\mathrm{o}}$ compose a dephase component, which can dephase the two-photon state into a completely mixed state ${\mathbb{I}}_4/4$. Module (c) is used to realize three Pauli measurements and reconstruct quantum states. Abbreviations: HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarizing beam splitter; BBO, type-I $\beta$-barium borate crystal; $\mathrm{YV}{\mathrm{O}}_4$, yttrium orthovanadate crystal; IF, interference filter; SPD, single photon detector.

Figure 2

The reconstructed density matrices of ${\rho }_1(\theta =22.5^{\mathrm{o}},\chi =1), {\rho }_2(\theta =7.5^{\mathrm{o}},\chi =1)$, and ${\rho }_3(\chi =0)$. $\mathrm{Re}(·)$ and $\mathrm{Im}(·)$ represent the real and imaginary parts of these states, respectively.

Figure 3

Experimental results and the corresponding theoretical predictions of LHS for the SCG and LSC. The red horizontal dashed-dotted line represents the bounds of the SCG for $q=2$ and the LSC. The blue horizontal dashed-dotted line represents the bound of the SCG for $q\to 1$.