Matej Pivoluska

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.

In our work, we provide a clean security analysis of a new high-dimensional QKD setup with a Franson interferometer in the asymptotic limit and calculate secure key rates using a recent method developed. We argue that our new protocol is not only experimentally easier, as it does not require tomography of the polarization degree of freedom, but also allows for a clean security analysis without assumptions that were implicitly hidden in earlier analyses of similar and related protocols. We build a realistic noise model that takes environmental photons, dark counts, channel losses and non-unit detection efficiency into account and show that our new protocol allows secure key rates for twice as many environmental photons than comparable protocols available in literature. We want to highlight that while the security analysis of our protocol is rigorous and clean, the compared key rates for the compared protocol are actually only an upper bound (due to the assumptions implicitly hidden described earlier), so our new protocol outperforms previous settings by at least a factor of 2. Current free-space QKD implementations are only operable during night when environmental photons are low, but fail to provide secure keys during twilight and daytime, which is a major obstacle towards broad practical usage. Thus, doubling the robustness against environmental photons marks an important step forwards towards daylight-independent Quantum Key Distribution implementations.

Satellite-based implementations are essential to realise QKD systems with global reach. Our current work aims to develop a consistent protocol that specifies the individual procedural steps of Decoy-State BB84 for space applications, accompanied by a rigorous security analysis. To this end, we are bringing together the results of decades of fundamental research and patching gaps where necessary to make it ready for application in accredited systems. On the poster, we will present interim results as well as the main challenges we are facing. For a more detailed abstract, please see the submitted pdf file above.