Pierre Pocreau

Abstract :
This thesis investigates two phenomena in the foundations of physics: nonlocality, explored through the study of entanglement in non-cooperative games; and the possibility for indefinite causal orders, challenging the common assumption that computations should be performed in a well-defined sequential order.
     Non-cooperative games are seldom encountered in quantum information theory but are common in game theory where the notion of Nash equilibrium arises. We analyse two types of quantum resources for these games. While these two resources are equivalent in cooperative settings, we show that they differ in games of conflicting interest where they lead to different Nash equilibria and solutions with potentially different social welfare.
     In the second part, we aim to obtain a better understanding of the computational power of indefinite causal orders. While the standard model of quantum circuits assumes operations are applied in a well-defined causal order, lately, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant attention via the higher-order framework of quantum supermaps. Quantum supermaps being best understood as a black-box model of computation, we start by extending the notion of query complexity of Boolean functions using supermaps as a generalised computational framework, both in the classical and quantum case. By extending these different measures of complexity to causally indefinite scenarios, we assess the limits and advantages of causally indefinite computations in a rigorous complexity-theoretic framework, the same in which the known separations between classical and quantum computers are usually framed.