Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long measurement times, and limited encoding capacity. At the same time, entanglement certification methods often rely on assumptions that compromise security. Here we show the certification of photonic high-dimensional entanglement in the transverse position-momentum degree-of-freedom with a record quality, measurement speed, and entanglement dimensionality, without making any assumptions about the state or channels. Using a tailored macro-pixel basis, precise spatial-mode measurements, and a modified entanglement witness, we demonstrate state fidelities of up to 94.4% in a 19-dimensional state-space, entanglement in up to 55 local dimensions, and an entanglement-of-formation of up to 4 ebits. Furthermore, our measurement times show an improvement of more than two orders of magnitude over previous state-of-the-art demonstrations. Our results pave the way for noise-robust quantum networks that saturate the information-carrying capacity of single photons.

High-dimensional entanglement promises to increase the information capacity of photons and is now routinely generated, exploiting spatiotemporal degrees of freedom of single photons. A curious feature of these systems is the possibility of certifying entanglement despite strong noise in the data. We show that it is also possible to exploit this noisy high-dimensional entanglement for quantum key distribution by introducing a protocol that uses multiple subspaces of the high-dimensional system simultaneously. Our protocol can be used to establish a secret key even in extremely noisy experimental conditions, where qubit protocols fail. To show that, we analyze the performance of our protocol for noise models that apply to the two most commonly used sources of high-dimensional entanglement: time bins and spatial modes.

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 quantum key distribution 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 introduce a family of quantum key distribution protocols for distributing shared random keys within a network of $n$ users. The advantage of these protocols is that any possible key structure needed within the network, including broadcast keys shared among subsets of users, can be implemented by using a particular multipartite high-dimensionally entangled quantum state. This approach is more efficient in the number of quantum channel uses than conventional quantum key distribution using bipartite links. Additionally, multipartite high-dimensional quantum states are becoming readily available in quantum photonic labs, making the proposed protocols implementable using current technology.

Quantum key distribution (QKD) allows unconditionally secure communication based on the laws of quantum mechanics rather than 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. We analyze the underlying mechanisms for QKD with temporally uniform pair-creation probabilities and develop a simple but accurate model to calculate optimal tradeoffs 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.