Towards more realistic costs of information processing in the quantum regime

Information and energy are intrinsically linked. The more information an experimenter holds about the state of a physical system, the more effectively it can be used to extract useful energy. Conversely, to force the system from an unknown state into a known state costs energy. Landauer's principle cements this connection: in erasing a bit of information, at least kT ln 2 of energy must be dissipated. With the advent of quantum technologies and as features of integrated circuits approach atomic scales, it is a good time to re-examine the relationship between energy and information in quantum contexts.
This project covers three main themes. The first examines the energy cost of quantum information operations. Unlike many previous treatments, it is not sufficient to transform the average density matrix of input signals to the average output, but instead each individual signal must be mapped correctly. By constructing optimal protocols, we quantify a uniquely quantum extra cost arising from this more constrained problem. The second part explores the energy cost of erasing classical information encoded in quantum dots, with reference to two experiments. In the first, work done on the dot is measured via back-action on the vibrations of a carbon nanotube. In agreement with a parallel theoretical investigation, the results indicate that lifetime broadening, a quantum strong coupling effect, dominates the exchange rate between work and information in the device. We also outline the design of an experiment into the effect of potential difference on erasure cost. Finally, we consider the role of particle exchange symmetry. We introduce a scheme in which symmetry is encoded into a latent degree of freedom, such that the statistics can interpolate between Bose-Einstein and Fermi-Dirac. We study the thermal properties of such a system, including ways in which a fermion-boson phase transition could aid the performance of thermodynamic cycles.