Coherence measures and optimal conversion for coherent states

Superposition is a critical property of quantum system resulting in quantum coherence and quantum entanglement. Quantum coherence and also entanglement provide the important resource for quantum information processing, for example, Deutschs algorithm, Shors algorithm, teleportation, superdense coding and quantum cryptography [1]. As with any such resource, there arises naturally the question of how it can be quantified and manipulated. Attempts have been made to find meaningful measures of entanglement [2, 3, 4, 5, 6, 7], and also to uncover the fundamental laws of its behavior under local quantum operations and classical communication (LOCC) [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. Recently, it has attracted much attention to quantify the amount of quantum coherence. In [13], the researchers established a quantitative theory of coherence as a resource following the approach that has been established for entanglement in [6]. They introduced a rigorous framework for quantification of coherence and proposed several measures of coherence, which