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.