Information-theoretic foundations of quantum interference

The field of quantum information explores how quantum can outperform classical physics at solving information-processing tasks, such as those found in cryptography, communication, metrology, and computing. What makes quantum mechanics so successful at dealing with these tasks are two intriguing features: quantum entanglement and quantum interference. While quantum entanglement is widely acknowledged as crucial to quantum advantages, its power has been adequately understood only thanks to the celebrated Bells theorem. Apart from its foundational relevance, the latter remarkably triggered novel ways of manipulating information based only on correlations between inputs and outputs of otherwise uncharacterized devices, or black boxes. This is the so-called device-independent information processing. In recent years, this approach has led to stunning cryptography, communication, and randomness generation applications. On the other hand, although highlighted as the core feature of quantum mechanics, the phenomenon of quantum interference has remained mainly within the grip of foundational investigations, with little focus on its potential applications. The main objective of our project is to fill this gap. We plan to develop a theoretical framework that will enable us to explore novel ways in which quantum interference can be used in information processing. Following how Bell`s theorem has given us a better understanding of quantum entanglement, we will develop a black-box formulation adequate for interference phenomena. Besides providing new insights into the differences between classical and quantum theory, this will lead to the development of new protocols based entirely on quantum interference and are expected to have applications in cryptography and communication.

This project has shown how quantum interference - one of the most characteristic features of quantum physics - can be understood and used as a resource for processing information. Quantum interference is the effect behind famous experiments such as the double-slit experiment, where a single quantum object can exhibit behaviours that are impossible in classical physics. While interference is often presented as a mysterious feature of the quantum world, our project aimed to describe it in a more general and operational way: not by relying on a detailed picture of waves, particles, or measuring devices, but by focusing on observable correlations between events. One of the central results of the project was the development of a theory-independent formulation of interference. This means that interference can be described in terms of measurable relations between observable quantities, rather than through assumptions about the internal workings of a particular physical theory. In this respect, the project follows the spirit of Bell's theorem, which made it possible to understand quantum entanglement through observable correlations alone. Our work provides an analogous step for quantum interference and helps clarify what distinguishes classical, quantum, and more general possible physical theories. Building on these developments, we investigated how interference can be used in communication and information-processing tasks. We studied situations in which information is distributed over distant locations and must be accessed by a single physical carrier, such as a particle. The results show that quantum systems can process such delocalized information more effectively than classical systems by leveraging quantum interference. The impact of this research is twofold. On the one hand, it provides a better understanding of the foundations of quantum interference as a core feature of quantum theory. On the other hand, it opens a new route towards quantum information-processing tasks based on interference, with potential applications in secure communication, cryptography, and quantum networks. The project also contributed to the training of young researchers and to public communication about why foundational research in quantum physics matters: today's abstract questions can become tomorrow's technological principles.