Indefinite causal orders in quantum mechanics

The premise of this project is that quantum mechanics forces us to abandon the notion of objective reality; the results of a measurement of a physical quantity, such as position or energy, cannot be understood as revealing a pre-existing value of that quantity, unless one is willing to accept paradoxical consequences such as contextuality. Quantum theory is better understood from an operational point of view: it provides the means to calculate outcome probabilities once given operations are performed. Nonetheless, the theory still assumes that space and time are fixed prior to and independent of any operation and measurement. This contrasts with the spirit of general relativity, which stipulates that geometrical quantities are not absolute, but rather represent the relations between operationally defined clocks, rods, etc. The goal of this project is to develop a consistent theoretical framework for quantum mechanics in which no prior geometrical notions are assumed, not even an underlying causal structure according to which events are ordered. Causal relations rather emerge operationally in the case where an agent send signals to another. It will be investigated how ordinary space-time can emerge within this framework, as well as the consequences that abandonment of a fixed causal structure has on quantum information processing. It will also be investigated where and how one can expect to find in nature instances of indefinite causal structures.