title: Quantum Enhanced Estimation of a Multidimensional Field.
abstract: We present a framework for the quantum enhanced estimation of multiple parameters corresponding to noncommuting unitary generators. Our formalism provides a recipe for the simultaneous estimation of all three components of a magnetic field. We propose a probe state that surpasses the precision of estimating the three components individually, and we discuss measurements that come close to attaining the quantum limit. Our study also reveals that too much quantum entanglement may be detrimental to attaining the Heisenberg scaling in the estimation of unitarily generated parameters.
authors: Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom.
authors: Tillmann
authors: T
authors: Baumgratz
authors: Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom.
authors: Animesh
authors: A
authors: Datta