Scientists Harness 19th-Century Optics To Advance Quantum Encryption

Researchers at the University of Warsaw have demonstrated a new approach to quantum key distribution that leverages high-dimensional encoding and a classical optical phenomenon known as the Talbot effect. By exploiting time-bin superpositions of photons, the system can transmit more information while relying on a surprisingly simple experimental setup built from commercially available components. Credit: Shutterstock A new quantum communication method uses the temporal Talbot effect to simplify high-dimensional quantum key distribution. As digital communication accelerates and cyber threats continue to rise, researchers are searching for safer ways to transmit sensitive information. One promising approach is quantum cryptography, which uses individual photons to generate encryption keys that cannot be secretly intercepted. Scientists at the Faculty of Physics at the University of Warsaw have now designed and tested a new system for quantum key distribution (QKD) within an urban fiber network. Their method uses what is known as high-dimensional encoding. The setup is simpler to construct and expand than many current systems, yet it relies on a physical phenomenon first described nearly 200 years ago, called the Talbot effect. The findings were published in the journals Optica Quantum, Optica, and Physical Review Applied. “Our research focuses on quantum key distribution (QKD) – a technology that uses single photons to establish a secure cryptographic key between two parties,” says Dr. Michał Karpiński, head of the Quantum Photonics Laboratory at the Faculty of Physics, University of Warsaw. “Traditionally, QKD employs so-called qubits – the simplest units of quantum information. While this method is already well tested, it does not always meet the requirements of more demanding applications. That’s why researchers are now working on multidimensional encoding. Instead of qubits, which yield one of two measurement outcomes, we use more complex quantum states that can take on multiple values.” At the Quantum Photonics Laboratory, researchers study time-bin superpositions of photons. In this situation, a photon is not strictly “earlier” or “later.” Instead, it exists in a combination of both states. When such a photon is detected, the exact arrival time appears random. Information is stored in the relationship between earlier and later light pulses, specifically in the phase of the light wave. “Until now, efficient detection of superpositions of two pulses – earlier and later – was possible. We went a step further: we are interested in cases with more time bins, ranging from two to four or even more,” adds Dr. Karpiński.

The Temporal Talbot Effect To accomplish this, the team turned to the Talbot effect, a phenomenon in classical optics first described in 1836 by photography pioneer Henry Fox Talbot. “When light passes through a diffraction grating, its image repeats itself at regular intervals – as if it ‘revives’ at a certain distance. Interestingly, the same effect occurs not only in space but also in time, provided that a regular train of light pulses propagates in a dispersive medium such as an optical fiber,” explains Maciej Ogrodnik, a PhD student at the Faculty of Physics, UW. Detection of time-bin superpositions with the temporal Talbot carpet. Credit: Maciej Ogrodnik, University of Warsaw “Thanks to the space-time analogy in optics, we can apply the Talbot effect to short light pulses, including single photons – thereby gaining new capabilities for analyzing and processing quantum states. In our case, a sequence of light pulses acts like a diffraction grating and can ‘self-reconstruct’ in time under dispersion after traveling some distance in an optical fiber. Moreover, the way pulses interfere depends on their phase, which allows us to detect different types of superpositions.” A Simpler Experimental Setup Using this concept, the researchers created an experimental four-dimensional QKD system. “Importantly, the entire setup is built using commercially available components. The key trick is that the system requires only a single photon detector to register superpositions of many pulses – instead of a complex network of interferometers,” says Adam Widomski, a PhD student at the Faculty of Physics, UW. “This significantly reduces the complexity and cost of the measurement system. Moreover, our method does not require separate, often time-consuming and challenging calibration of the receiver.” “Traditionally, to detect phase differences between pulses, we use a multi-interferometer setup – something like a tree, where pulses are split and delayed. Unfortunately, such systems are inefficient, since some measurement outcomes are useless. The efficiency drops with the number of pulses, and the receiver requires precise calibration and stabilization,” explains Ogrodnik. “The advantage of our method is its high efficiency, as all photon detection events are useful. The drawback is relatively high measurement error rates. However, these do not prevent QKD, as we showed in collaboration with researchers working on the theory of quantum cryptography. Furthermore, we do not need to rebuild the setup for different dimensions of superpositions – we can detect 2D and 4D superpositions without changing hardware or stabilizing the receiver. This is a huge advantage compared to earlier methods,” adds Widomski.

Not Only Speed, But Also Security The team tested the system in both laboratory optical fibers and the existing fiber network at the University of Warsaw, covering distances of several kilometers. “Thanks to the new method using the temporal Talbot effect, we successfully demonstrated QKD with two- and four-dimensional encoding, using the same transmitter and receiver. Despite errors inherent to the simple experimental approach, our results confirm the higher information efficiency of the system resulting from high-dimensional encoding,” says Widomski. A major strength of QKD is that its security can be mathematically proven under basic assumptions. Because of this, the Warsaw researchers worked from the beginning with collaborators in Italy and Germany who specialize in QKD security analysis. “A closer analysis shows that the standard description of many QKD protocols is incomplete, which attackers could exploit. Unfortunately, our method shares this vulnerability. We took part in efforts to solve this issue. Our collaborators found that a certain modification of the receiver allows for collecting more data, thus eliminating the vulnerability. The security proof of the new protocol was published in Physical Review Applied, and in our latest paper, we discuss its application to our experiment,” says Ogrodnik. References: “High-dimensional quantum key distribution with resource-efficient detection” by Maciej Ogrodnik, Adam Widomski, Dagmar Bruẞ, Giovanni Chesi, Federico Grasselli, Hermann Kampermann, Chiara Macchiavello, Nathan Walk, Nikolai Wyderka and Michał Karpiński, 24 August 2025, Optica Quantum. DOI: 10.1364/OPTICAQ.560373 “Efficient detection of multidimensional single-photon time-bin superpositions” by Adam Widomski, Maciej Ogrodnik and Michał Karpiński, 19 July 2024, Optica. DOI: 10.1364/OPTICA.503095 “Quantum key distribution with basis-dependent detection probability” by Federico Grasselli, Giovanni Chesi, Nathan Walk, Hermann Kampermann, Adam Widomski, Maciej Ogrodnik, Michał Karpiński, Chiara Macchiavello, Dagmar Bruß and Nikolai Wyderka, 4 April 2025, Physical Review Applied. DOI: 10.1103/PhysRevApplied.23.044011 The project was carried out within the QuantERA international cooperation program on quantum technologies, coordinated by the National Science Centre (NCN, Poland). The research used infrastructure of the National Laboratory for Photonics and Quantum Technologies (NLPQT) at the Faculty of Physics, University of Warsaw.