title: Probabilistic metrology attains macroscopic cloning of quantum clocks.
abstract: It has recently been shown that probabilistic protocols based on postselection boost the performances of the replication of quantum clocks and phase estimation. 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 state 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 when the performance of the simulation is measured by testing small groups of clones.
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
authors.forename: B
authors.initials: B
authors.lastname: Gendra
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
authors.forename: J
authors.initials: J
authors.lastname: Calsamiglia
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
authors.forename: R
authors.initials: R
authors.lastname: Muñoz-Tapia
authors.affiliation: Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain and Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
authors.forename: E
authors.initials: E
authors.lastname: Bagan
authors.affiliation: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China.
authors.forename: G
authors.initials: G
authors.lastname: Chiribella