Dr. Kyrylo Simonov

Higher-order maps without causal order: Applications to quantum information, cryptography, and thermodynamics

The nature of causality remains one of the key puzzles in science. In quantum theory, the causal structure is not subject to quantum uncertainty and plays rather a background role. One can ask whether the background causal structure can be dropped, for example, by respecting causality only locally. Such scenarios of local validity of quantum theory while relaxing the global definite causal order of operations can be described via the machinery of higher-order operations, i.e. supermaps. An important example of scenarios of this kind is quantum SWITCH, a process realizing a quantum superposition of causal orders of operations. Looking for the possible applications of quantum SWITCH has been the subject of growing interest in the scientific community as it could provide communication and computational resources not realizable via standard quantum theory. Moreover, very recently, the benefits potentially offered by quantum SWITCH for thermodynamic and cryptographic tasks have appeared in the spotlight. My talk aims at highlighting the benefits and applications of higher-order maps to information processing, cryptography, and thermodynamics.