Iman Marvian

The problem of coherence distillation asks: given multiple copies of a coherent input state, produce a coherent output state with much less noise (that is, much closer to a pure coherent state), in such a way that the time evolution of the output state matches the time evolution of the input state. We thoroughly address this problem for the case of qubit states. Principally, we compute the distillation channel that is asymptotically optimal in the limit of a large number of input qubit states and compute the resulting infidelity (one minus fidelity) between the output qubit state and the desired pure state. We show that this infidelity is closely related to a resource known as purity of coherence, a quantity obtained from the Right Logarithmic Derivative (RLD) Fisher information metric. We thus demonstrate an operational meaning for purity of coherence as the quantity whose monotonicity on time-translation invariant channels sets the strongest asymptotic bound on the capability of coherence distillation for qubit states. For a special choice of input and output state, we additionally investigate a number of extensions of this primary result. In particular, we present numerical schemes to produce the exact optimal distillation protocol for a fixed value of $N$, extend the computation of the optimal protocol and the minimum infidelity to the $1/N^2$ and $1/N^3$ orders, estimate the amount of purity of coherence that is dissipated by the optimal distillation protocol, and compute the mathematical behavior of the protocol more precisely in the low-noise and high-noise limits.

Finding the consequences of symmetries in dynamics is a subject with broad applications in physics. We are interested to find tools to study the consequences of symmetry which apply to open as well as closed quantum systems. We introduce a different point of view for thinking about asymmetry which is not based on symmetric dynamics; instead it is based on the intuition that a state which breaks symmetry can be thought as a signal which carries information about the group element. Using this point of view we use information measures to build asymmetry measures via the Holevo quantity. We show that for pure states Noether's theorem includes all the possible implications of the symmetry of dynamics, but for mixed states conservation of asymmetry measures imply more constraints than those prescribed by Noether's theorem.