title: Joint estimation of phase and phase diffusion for quantum metrology.
abstract: Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states--split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental set-up for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.
authors.affiliation: 1] QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, UK [2] Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK.
authors.forename: Mihai D
authors.initials: MD
authors.lastname: Vidrighin
authors.affiliation: Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK.
authors.forename: Gaia
authors.initials: G
authors.lastname: Donati
authors.affiliation: 1] QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, UK [2] Department of Physics & Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
authors.forename: Marco G
authors.initials: MG
authors.lastname: Genoni
authors.affiliation: 1] Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK [2] Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Xian-Min
authors.initials: XM
authors.lastname: Jin
authors.affiliation: Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK.
authors.forename: W Steven
authors.initials: WS
authors.lastname: Kolthammer
authors.affiliation: QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, UK.
authors.forename: M S
authors.initials: MS
authors.lastname: Kim
authors.affiliation: Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK.
authors.forename: Animesh
authors.initials: A
authors.lastname: Datta
authors.affiliation: Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK.
authors.forename: Marco
authors.initials: M
authors.lastname: Barbieri
authors.affiliation: Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, UK.
authors.forename: Ian A
authors.initials: IA
authors.lastname: Walmsley