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

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.

💡 Research Summary

The paper presents the first experimental demonstration of certifying ensembles of high‑dimensional quantum states using independent preparation and measurement devices, i.e., devices that share no common randomness. The authors adopt a semi‑device‑independent (SDI) framework in which the only trusted assumption is the Hilbert‑space dimension of the prepared states. Within this framework they implement a randomized unambiguous state discrimination (USD) protocol: Alice randomly selects two inputs (x_1<x_2) and prepares the corresponding pure states (|\psi_{x_1}\rangle,|\psi_{x_2}\rangle); Bob randomly chooses a measurement setting (y) and obtains one of three outcomes ({-1,+1,\perp}), where (\perp) denotes an inconclusive result. The protocol defines an inconclusive‑event rate (p^{\text{usd}}_{x_1,x_2}) and a cumulative quantity (S_t) that aggregates the squared deviations of these rates over all ordered pairs ((x_1,x_2)). For a given dimension (d), ensemble size (N) and order (t), the minimal achievable (S_t) is attained when the prepared states form a quantum (t)-design. In particular, for (t=2) and (N=d^2) the optimal design corresponds to a symmetric informationally complete (SIC) set. The theoretical lower bound on (S_t) (Eq. 4 in the paper) can be saturated only by such a SIC ensemble, providing a clear certification criterion.

Experimentally, the authors generate high‑dimensional orbital angular momentum (OAM) states of single photons. A 405 nm laser pumps a PPKTP crystal inside a Sagnac interferometer to produce photon pairs at 810 nm via spontaneous parametric down‑conversion. One photon serves as a herald; the other is sent through two phase‑only spatial light modulators (SLM1 for state preparation, SLM2 for measurement). Optimized computer‑generated holograms, based on the method of Ref.