QUROPE Quantum Information Processing and Communication in Europe

Objectives: The development of quantum technologies has been driven by theoretical work of scientists working on the boundary between Physics, Computer Science, Mathematics, and Information Theory. In the early stages of this development, theoretical work has often been far ahead of experimental realization of these ideas. At the same time, theory has provided a number of proposals of how to implement basic ideas and concepts from quantum information in specific physical systems. These ideas are now forming the basis for successful experimental work in the laboratory, driving forward the development of tools that will in turn form the basis for all future technologies which employ, control and manipulate matter and radiation at the quantum level.

State of the art: in recent years, novel theoretical ideas have been proposed, extending the range of applicability of quantum information protocols. The novel scenario of device-independent quantum information processing has emerged, where protocols are defined independently of the inner working of the devices used in the implementation. This new approach has led to self-certified schemes for QKD and randomness generation. A strong theoretical effort has opened quantum simulation to quantum field theories and quantum chemistry. From a purely information theory point of view, non-additivity effects of channel capacities with no classical analogue have been proven. Finally, quantum information theory has established strong bridges with other fields, such as condensed matter, quantum thermodynamics, biology or quantum gravity. The study of topological systems for quantum information purposes, the development of novel numerical methods for the classical simulation of many-body quantum systems, the study of Hamiltonian complexity or, more recently, the use of quantum information techniques for a better understanding of the physics of black holes, as well as applications in mathematics and computer science, are examples of these synergies.

Future directions: the impressive experimental progress in controlling quantum particles has brought the field to a regime where experimental setups can hardly be simulated in existing classical computing devices. The design of methods to estimate, control and certify these complex setups is essential for the development of the field. Also, we expect quantum information theory to extend and strengthen its applicability to other fields, providing new insights in quantum thermodynamics, many-body physics or quantum gravity. The recent device-independent scenario, in which protocols are defined independently of the inner working of the devices, also offers promising perspectives, especially for cryptographic applications.

Relevant research directions for the next years include:

• Methods for the reconstruction and estimation of complex quantum states or channels beyond tomography protocols, which are as hard as simulating a quantum system classically.
• Methods for the certification and validation of quantum processes; benchmarking of purely quantum effects with no classical analogue.
• Methods for error correction beyond quantum computation and study of their application to quantum simulation, communication or sensing.
• Methods for the control of complex quantum setups.
• Development of device-independent solutions: novel protocols, general framework for security analysis in this approach or feasible proposals for their experimental realization.
• Novel applications of quantum information concepts in other fields, such as thermodynamics, many-body systems, mathematics, computer science, biology, quantum chemistry, high-energy physics or quantum gravity.
• Development of undecidability theory.