Entropic inequalities and the ultimate limits of information transmission with bosonic systems – BOSONENT

Photonic quantum technologies promise revolutionary applications such as high-speed, long-distance, and ultra-secure communication over an envisioned quantum internet. Non-Gaussian bosonic systems are required for crucial quantum information processing tasks and without them we lose many significant advantages offered by quantum mechanics. However, they are poorly understood theoretically. The major challenge BOSONENT faces is the computation of the capacities of non-Gaussian channels, i.e. the highest (quantum-limited) achievable rates at which they reliably transmit information. Their knowledge will be crucial to build photonic communication systems. BOSONENT will address this challenge by offering a deep characterisation of non-Gaussian channels for information transmission. BOSONENT has three main objectives, each one representing a major contribution to the field: (i) we will develop novel theoretical instruments to characterise non-Gaussian bosonic systems, especially their entropies, which provide expressions for capacities; (ii) we will prove carefully chosen entropic inequalities to reveal the behaviour of information in bosonic communication channels; (iii) we will provide formulas and bounds for capacities of non-Gaussian bosonic channels, such as classical, quantum, and private capacities. Preliminary generating function methods I have developed to describe the information-theoretic properties of non-Gaussian systems show great promise in tackling the problems at hand and set the cornerstone of the project. Such novel methodologies represent a strong disruption in the current approaches, which are limited to tools efficient only in the much simpler Gaussian scenario. Significant impacts beyond quantum communication, e.g. in quantum computation with boson samplers and bosonic qubits, are anticipated as well. BOSONENT will also contribute to the foundations of a much-anticipated quantum internet by orienting the design of large-scale communication schemes.