Large consequences of quantum coherence in small systems

This thesis is concerned with the theoretical behaviour and interactions of quantum systems. It is composed of three main parts. We begin by investigating the correlations attainable when a bipartite quantum system undergoes unitary dynamics. The correlations are quantified by the quantum mutual information. We fully solve the problem for the smallest system of two qubits and present work towards solving the general case. The optimisation can be applied to thermodynamic scenarios, for example, heat exchange between two quantum systems. More specifically, we find bounds any negative heat flow from cold to hot, which can occur if the systems are initially correlated. We also present related applications such as a generalized collision model approach to thermal equilibrium, and a situation where a global Maxwell demon can play tricks on a local observer by reversing their local arrow of time. Experimental evidence suggests that biology may harness quantum effects to improve the efficiency of some of its processes. One such process is hydrogen transfer, catalysed by an enzyme called soybean lipoxygenase. The observed rates for this reaction strongly indicate that the hydrogen could be tunnelling through the energy barrier. We study this reaction by designing a qualitative model and find that our rates exhibit similar trends to those seen in experiments. The final part of the thesis is concerned with the quantum steering ellipsoid: a faithful, three-dimensional (3D) representation for the state of a two-qubit system. The steering ellipsoid is the set of states that Bob can collapse Alice's qubit to when he performs all possible measurements on his qubit. This formalism leads to numerous new features. We uncover a notion of incomplete steering of a separable state; geometric necessary and sufficient conditions for entanglement and discord; and a volume formula for the ellipsoid that identifies when steering is 3D, giving rise to a new type of correlation called "obesity".Open Acces