Are cloned quantum states macroscopic?

TL;DR

This paper examines whether quantum states produced by optimal phase covariant cloning are truly macroscopic superpositions, concluding they are not, but the cloned states themselves are macroscopic and useful in quantum metrology.

Contribution

The study distinguishes between macroscopic superpositions and cloned states, showing cloned states are macroscopic and effective for quantum metrology despite not being macroscopic superpositions.

Findings

Cloned superpositions are not macroscopic in the Schrödinger's cat sense.

Cloned quantum states are macroscopic according to multiple measures.

Cloned states are effective for quantum parameter estimation.

Abstract

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 Schr\"odinger'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.