Tight bounds on the simultaneous estimation of incompatible parameters

Jasminder S. Sidhu, Yingkai Ouyang, Earl T. Campbell, Pieter Kok

Research output: Working paper

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The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables has greatly diminished the applicability of estimation theory in many practical implementations. The Holevo Cramer-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multi-parameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimisation over multiple variables. In this work, we show that the HCRB can be solved analytically for two parameters. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations. We apply our formalism to magnetic field sensing. Our results provide fundamental insight and make significant progress towards the estimation of multiple incompatible observables.
Original languageEnglish
Place of PublicationIthaca, New York
Number of pages24
Publication statusPublished - 6 Aug 2020

Publication series

Publisher[Ithaca, N.Y.] : Cornell University [1991]-
ISSN (Print)2331-8422


  • quantum metrology
  • quantum information processing
  • Holevo Cramer-Rao bound (HCRB)


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