title: Fisher-Symmetric Informationally Complete Measurements for Pure States.
abstract: We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that uniquely represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete-i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states-and it is maximal in the sense of a multiparameter quantum Cramér-Rao bound. For a d-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below 4d-3, for the usual notion of global pure-state informational completeness, to 2d-1.
authors.affiliation: Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA.|Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Nan
authors.initials: N
authors.lastname: Li
authors.affiliation: Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA.|Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia.
authors.forename: Christopher
authors.initials: C
authors.lastname: Ferrie
authors.affiliation: Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA.
authors.forename: Jonathan A
authors.initials: JA
authors.lastname: Gross
authors.affiliation: Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA.
authors.forename: Amir
authors.initials: A
authors.lastname: Kalev
authors.affiliation: Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131-0001, USA.|Centre for Engineered Quantum Systems, School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia.
authors.forename: Carlton M
authors.initials: CM
authors.lastname: Caves