Experimental certification of ensembles of high-dimensional quantum states with independent quantum devices

Abstract

When increasing the dimensionality of quantum systems, high-dimensional quantum state certification becomes important in quantum information science and technology. However, how to certify ensembles of high-dimensional quantum states in a black-box scenario remains a challenging task. In this work, we report an experimental test of certifying ensembles of high-dimensional quantum states based on prepare-and-measure experiments with \textit{independent devices}, where the state preparation device and the measurement device have no shared randomness. In our experiment, the prepared quantum states are high-dimensional orbital angular momentum states of single photons, and both the preparation fidelity and the measurement fidelity are about 99.0$\%$ for the six-dimensional quantum states. We also measure the crosstalk matrices and calculate the similarity parameter for up to ten dimensions. We not only experimentally certify the ensemble of high-dimensional quantum states in a semi-device-independent manner, but also experimentally investigate the effect of atmospheric turbulent noise on high-dimensional quantum state certification. Our experimental results clearly show that the certification of high-dimensional quantum states can still be achieved even under the influence of atmospheric turbulent noise. Our findings have potential implications in quantum certification and quantum random number generation.

Figures (5)

• Figure 1: Randomized unambiguous state discrimination.
• Figure 2: Experimental setup for certifying ensembles of states with independent devices. The heralding photon, produced by spontaneous parametric down-conversion, is directly sent to a detector which acts as a trigger. The signal photon is projected on the fundamental Gaussian state by means of a single mode fiber. In order to make full use of the SLM, we use two lenses to expand the laser beam. To avoid the Gouy phase shift effect, an imaging $4f$ system is implemented between the screens of the two spatial light modulators. PBS stands for polarization beam splitter; Di for dichroic; DM for dichroic mirror; and IF for interfering filter.
• Figure 3: Experimental analysis of different OAM photonic qudit states. (a) Cross-talk matrix between the different OAM modes. (b) Experimentally produced intensity profiles of the OAM quantum states used in our experiment.
• Figure 4: Experimental results of certifying high-dimensional quantum states with independent devices. In our experiment, we certify high-dimensional quantum states with dimensions 2-10. We randomly prepare initial states and measure them on different bases. Once the measured values of $S_{2}$ are equal to the theoretical values, we can determine which quantum states the initial states correspond to.
• Figure 5: Certifying high-dimensional quantum states under the effects of atmospheric turbulence. We investigate the relationship between $S_{\epsilon}$ and the error rate $\epsilon$. Atmospheric turbulent noise affects Bob's error rate $\epsilon$. As the error rate $\epsilon$ increases, the value of $S_{\epsilon}$ gradually increases. The theoretical predictions are in good agreement with the experimental results.