As digital communications evolve and the number of cyber threats increases, researchers are developing new methods for secure data transmission. One of the most promising directions is quantum cryptography, which uses individual photons to generate encryption keys. A team of specialists from the Faculty of Physics at the University of Warsaw has developed and tested a new quantum key distribution (QKD) system, applying it to existing urban fiber-optic networks. Their approach is based on multidimensional encoding and the use of an optical phenomenon known as the Talbot effect.

Quantum Key Distribution and Multidimensional Encoding

Quantum key distribution (QKD) is a technology that enables the establishment of a secure cryptographic key between two parties using single photons. Traditionally, this is achieved with qubits—the simplest units of quantum information, which yield one of two possible measurement outcomes. However, for more complex tasks, methods of multidimensional encoding are being developed, where quantum states can take on several values. In laboratory settings, researchers study superpositions of photon time bins, where a photon can exist as a combination of "early" and "late" states. Information is encoded in the phase relationship between light pulses, and the exact detection time of a photon is random. Previously, only superpositions of two pulses were effectively recorded, but now cases with a greater number of time bins—from two to four and more—are being explored.

Application of the Talbot Effect

In their work, the team utilized the Talbot effect—a classical optical phenomenon first described in 1836. When light passes through a diffraction grating, its image periodically repeats at certain distances. This effect manifests not only in space but also in time if a regular sequence of light pulses propagates through a dispersive medium such as optical fiber. By applying this effect to sequences of light pulses, including single photons, the researchers created a system in which signals can self-reconstruct in time as they travel through the fiber. The nature of the overlap and interference of pulses depends on their phase, allowing different quantum states to be distinguished and measured.

Design Features and Advantages

The experimental QKD system built by the researchers operates in four dimensions and is assembled from commercially available components. To register superpositions of multiple pulses, only one photon detector is required, which simplifies the design and reduces costs compared to traditional systems that use complex interferometer networks. This approach also eliminates the need for frequent and precise receiver calibration.

In traditional schemes, multi-interferometric systems are used to detect phase differences between pulses, but part of the measurement results becomes unusable, and efficiency decreases as the number of pulses increases. The new method stands out for its high efficiency, as all photon detection events are utilized. Despite a relatively high probability of measurement errors, this does not hinder QKD operation, as confirmed by joint research with quantum cryptography theorists. Moreover, the system does not require retuning to work with different superposition sizes—2D and 4D superpositions can be detected without changing the hardware or stabilizing the receiver.

Testing and Security Considerations

The system was tested both in laboratory conditions and in a real fiber network at the University of Warsaw over several kilometers. The new method, based on the temporal Talbot effect, enabled the demonstration of QKD with two- and four-dimensional encoding using the same transmitter and receiver. Despite errors inherent to the experimental approach, the results confirmed the system’s higher information efficiency thanks to multidimensional encoding.

Quantum key distribution is valued for its provable security under certain assumptions. To verify the reliability of the approach, an analysis was conducted together with international QKD security experts. It was found that the standard description of many QKD protocols is incomplete, which could be exploited by attackers. The new method is also subject to this vulnerability; however, modifying the receiver allows for the collection of more data and resolves the issue. The security proof for the new protocol has been published, and its application to the experiment is discussed in the latest work.

Prospects for Quantum Photonics Development

In addition to demonstrating a new communication method, the project contributed to the development of quantum photonics expertise at the University of Warsaw. The work was carried out as part of the international QuantERA program on quantum technologies, coordinated by the National Science Centre of Poland, and also utilized resources from the National Laboratory for Photonics and Quantum Technologies at the university’s Faculty of Physics.