Quantum coherence manipulation with finite resources

Kun Fang, University of Cambridge

As a more general form of quantum superposition, quantum coherence represents one of the most fundamental features that set the difference of quantum mechanics from the classical realm. In this talk, we will use the tool of semidefinite programming to study two fundamental tasks relating quantum coherence, i.e., coherence distillation of quantum states and coherence cost of quantum processes. The first task investigates the maximum number of coherent bits (cobits) can be extracted from a given quantum state while the second one discusses the minimum number of cobits required to simulate a quantum process. Both tasks are explored in the one-shot setting with finite resources, and efficiently computable results are provided.