Roman Solar

We investigate the practical requirements for certifying high-dimensional quantum entanglement using existing matrix completion techniques. Focusing on time-bin entangled systems, we simulate the measurement of selected diagonals of the density matrix to identify minimal yet effective configurations. Our results indicate that measuring the main diagonal along with just two off-diagonals is often sufficient to tightly lower-bound the Schmidt number, entanglement of formation, and distillable secret key rate. We further develop a method for selecting an optimal set of diagonals based on the dimension of the system - corresponding to an optimal choice of interferometer delays. This work offers experimental guidance for efficient entanglement certification in high-dimensional quantum systems.

This work introduces a novel approach to certifying high-dimensional quantum entanglement using matrix completion methods. Instead of relying on complete state tomography, our method measures select elements of the density matrix and completes the remaining elements through convex optimization to minimize the entanglement measure. This allows us to compute a lower bound for the Schmidt number and the entanglement of formation, providing a practical alternative to traditional techniques. Our approach is flexible and does not require measurements in specific bases, making it particularly advantageous for time-bin entanglement scenarios.