  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.
