Probabilistic Metrology Attains Macroscopic Cloning of Quantum Clocks

TL;DR

This paper shows that probabilistic quantum metrology can achieve macroscopic cloning of quantum clocks, with performance limits tied to the clock's Hamiltonian properties, maintaining the equivalence between cloning and estimation asymptotically.

Contribution

It establishes the conditions under which probabilistic metrology attains macroscopic cloning, highlighting the role of eigenvalue independence and simulation capabilities.

Findings

Cloning fidelity depends on the rational independence of Hamiltonian eigenvalues.

Asymptotic cloning and estimation performances match in the macroscopic limit.

Probabilistic metrology can simulate cloning for arbitrary states when performance is tested on small groups.

Abstract

It has been recently shown that probabilistic protocols based on postselection boost the performances of phase estimation and the replication of quantum clocks. Here we demonstrate that the improvements in these two tasks have to match exactly in the macroscopic limit where the number of clones grows to infinity, preserving the equivalence between asymptotic cloning and estimation for arbitrary values of the success probability. Remarkably, the cloning fidelity depends critically on the number of rationally independent eigenvalues of the clock Hamiltonian. We also prove that probabilistic metrology can simulate cloning in the macroscopic limit for arbitrary sets of states, provided that the performance of the simulation is measured by testing small groups of clones.