Ty Volkoff, University of California, Berkeley
Two measures of macroscopicity for quantum superpositions in countably infinite dimensional Hilbert space will be introduced: one depending on the optimal distinguishability of the components of the superposition under measurements of subsets of particles and another based on the ratio of the quantum Fisher information of the superposition to that of its components. For a large class of superpositions, which includes many Schrodinger cat states, these measures are equivalent, and I will argue that "large" quantum superpositions in this class can be considered as valuable resources (distinct from entangled states) for high-precision quantum metrology. Examples will be taken from multimode quantum optics, BECs, and (2+1)-dimensional quantum dimers. I will show that the maximal metrological usefulness of a Schrodinger cat state compared to its two branches depends on the Lie algebra containing the observables of the system and I will provide a method for constructing the optimal Lie algebra by compressing unbounded observables to a subspace containing the cat state