Are cloned quantum states macroscopic?

We study quantum states produced by optimal phase covariant quantum cloners. We argue that cloned quantum superpositions are not macroscopic superpositions in the spirit of Schrödinger's cat, despite their large particle number. This is indicated by calculating several measures for macroscopic superpositions from the literature, as well as by investigating the distinguishability of the two superposed cloned states. The latter rapidly diminishes when considering imperfect detectors or noisy states and does not increase with the system size. In contrast, we find that cloned quantum states themselves are macroscopic, in the sense of both proposed measures and their usefulness in quantum metrology with an optimal scaling in system size. We investigate the applicability of cloned states for parameter estimation in the presence of different kinds of noise.

Stable macroscopic quantum superpositions.

We study the stability of superpositions of macroscopically distinct quantum states under decoherence. We introduce a class of quantum states with entanglement features similar to Greenberger-Horne-Zeilinger (GHZ) states, but with an inherent stability against noise and decoherence. We show that in contrast to GHZ states, these so-called concatenated GHZ states remain multipartite entangled even for macroscopic numbers of particles and can be used for quantum metrology in noisy environments. We also propose a scalable experimental realization of these states using existing ion-trap setups.