Matej Pivoluska

Entanglement based quantum communication offers an increased level of security in practical secret shared key distribution. One of the fundamental principles enabling this security -- the fact that interfering with one photon will destroy entanglement and thus be detectable -- is also the greatest obstacle. Random encounters of traveling photons, losses and technical imperfections make noise an inevitable part of any quantum communication scheme, severely limiting distance, key rate and environmental conditions in which QKD can be employed. Using photons entangled in their spatial degree of freedom, we show that the increased noise resistance of high-dimensional entanglement, can indeed be harnessed for practical key distribution schemes. We perform quantum key distribution in eight entangled paths at various levels of environmental noise and show key rates that, even after error correction and privacy amplification, still exceed 1 bit per photon pair and furthermore certify a secure key at noise levels that would prohibit comparable qubit based schemes from working.

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.

Quantum Key Distribution (QKD) allows unconditionally secure communication based on the laws of quantum mechanics rather then assumptions about computational hardness. Optimizing the operation parameters of a given QKD implementation is indispensable in order to achieve high secure key rates. So far, there exists no model that accurately describes entanglement-based QKD with continuous-wave pump lasers. For the first time, we analyze the underlying mechanisms for QKD with temporally uniform pair-creation probabilities and develop a simple but accurate model to calculate optimal trade-offs for maximal secure key rates. In particular, we find an optimization strategy of the source brightness for given losses and detection-time resolution. All experimental parameters utilized by the model can be inferred directly in standard QKD implementations, and no additional assessment of device performance is required. Comparison with experimental data shows the validity of our model. Our results yield a tool to determine optimal operation parameters for already existing QKD systems, to plan a full QKD implementation from scratch, and to determine fundamental key rate and distance limits of given connections.

High-dimensional entanglement promises to increase the information capacity of photons and isnow routinely generated exploiting spatio-temporal degrees of freedom of single photons. A curiousfeature of these systems is the possibility to certify entanglement despite strong noise in the data.We show that it is also possible to exploit this noisy entanglement by introducing a protocol thatuses mutliple subspaces of the high-dimensional system simultaneously. Our protocol can be used toincrease key rates in realistic conditions. To that end, we conduct two simulations of our protocol fornoise models that apply to the two most commonly used sources of high-dimensional entanglement:time-bins and spatial modes.

Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Device-independent quantum random number generators (QRNGs) provide a means of completely trusted randomness, but are highly impractical due to their strict technological requirements, such as loophole-free quantum nonlocality. By making fixed assumptions on specific parts of the device, semi-device-independent QRNGs lower these requirements drastically. However, this {has usually been} done at the cost of limiting their flexibility and security to a specific physical implementation and level of trust. Here we propose and experimentally test a new framework for semi-device-independent randomness certification that employs a flexible set of assumptions, allowing it to be applied in a range of physical scenarios involving both quantum and classical entropy sources. At the heart of our method lies a source of trusted vacuum in the form of a signal shutter, which enables the honesty of partially trusted measurement devices to be tested and provides lower bounds on the guessing probability of their measurement outcomes. We experimentally verify our protocol with a photonic setup and generate secure random bits under three different source assumptions with varying degrees of security and resulting data rates. Our work demonstrates a simple and practical way for achieving semi-device-independent randomness generation with user-defined flexibility in terms of levels of trust and physical implementations.