1 / 21

R. Demkowicz-Dobrzański 1 , J. Kołodyński 1 , M. Guta 2

Quantum metrology and the geometry of quantum channels the illusion of the Heisenberg scaling. R. Demkowicz-Dobrzański 1 , J. Kołodyński 1 , M. Guta 2 1 Faculty of Physics , Warsaw University , Poland 2 School of Mathematical Sciences , University of Nottingham , United Kingdom.

cwen
Download Presentation

R. Demkowicz-Dobrzański 1 , J. Kołodyński 1 , M. Guta 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Quantum metrology and the geometry of quantum channels the illusion of the Heisenberg scaling R. Demkowicz-Dobrzański1, J. Kołodyński1, M. Guta2 1Faculty of Physics, Warsaw University, Poland 2 School of Mathematical Sciences, University of Nottingham, United Kingdom

  2. Interferometry atits (classical) limits LIGO - gravitationalwavedetector NIST - Cs fountainatomicclock Michelson interferometer Ramsey interferometry Precision limited by:

  3. N independent photons thebestestimator: Estimatoruncertainty: Standard Quantum Limit (Shotnoise limit)

  4. Entanglementenhanced precision Hong-Ou-Mandelinterference &

  5. Entanglementenhanced precision NOON states Estimator State preparation Measuremnt Heisenberg limit Standard Quantum Limit

  6. Whatarethefundamentalbounds inpresence of decoherence?

  7. General schemein q. metrology Input state of Nparticles phaseshift + decoherence measurement estimation Interferometerwithlosses (gravitationalwavedetectors) Qubitrotation + dephasing (atomicclockfrequencycallibrations)

  8. Localapproachusing Fisher information Cramer-Raobound: F – Fisher information (dependsonly on theinput state) No decoherence Withdecoherence • - Theoutput state ismixed • - Fisher Information, difficult to calculate • Optimalstates do not havesimplestructure Heisenberg scalingislosteven for infinitesimaldecoherence!!! • - OptimalNphoton state (maximalF=N2): • RDD, et al. PRA 80, 013825(2009), • U. Dorner, et al., PRL. 102, 040403 (2009) - Asymptoticanalyticallowerbound: J. Kolodynski, RDD, PRA 82,053804 (2010), S. Knysh, V. Smelyanskiy, G. Durkin PRA 83, (2011) B. M. Escher, et al.Nature Physics, 7, 406 (2011) (minimizationoverdifferent Kraus representations) Heisenberg scaling J. J. . Bollinger, W. M. Itano, D. J. Wineland, andD. J. Heinzen, Phys. Rev. A 54, R4649 (1996).

  9. Maximal quantum enhancement

  10. Heisenberg scalingislosteven for infinitesimaldecoherence!!! Canyouprove simpler, more general and moreintutive? Yes!!!

  11. Classicalsimulation of a quantum channel Convex set of quantum channels

  12. Classicalsimulation of a quantum channel Convex set of quantum channels Parameterdependencemoved to mixingprobabilities Before: After: By Markov property…. • K. Matsumoto, arXiv:1006.0300 (2010)

  13. Classicalsimulation of Nchannelsusedinparallel

  14. Classicalsimulation of Nchannelsusedinparallel =

  15. Classicalsimulation of Nchannelsusedinparallel =

  16. Precision boundsthanks to classicalsimulation • For unitarychannels Heisenberg scalingpossible • Generlicdecoherence model will manifest shotnoisescaling • To getthetighestbound we need to findtheclassicalsimulationwithlowestFcl

  17. The „Worst” classicalsimulation Quantum Fisher Informationat a givendependsonly on Itisenough to analize,,localclassicalsimulation’’: The „worst” classicalsimulation: Works for non-extremalchannels RDD,J. Kolodynski, M. Guta arXiv:1201.3940 (2012)

  18. Dephasing: derivation of theboundin 60 seconds! dephasing Choi-Jamiołkowskiisomorphism (positivieoperatorscorrespond to physicalmaps) RDD,J. Kolodynski, M. Guta, arXiv:1201.3940 (2012)

  19. Dephasing: derivation of theboundin 60 seconds! dephasing Choi-Jamiołkowskiisomorphism (positivieoperatorscorrespond to physicalmaps) RDD, J. Kolodynski, M. Guta, arXiv:1201.3940 (2012)

  20. Summary • Heisenberg scalingislost for a genericdecoherence channel even for infinitesimalnoise • Simple bounds on precision can be derivedusingtheclassicalsimulationidea • In caseclassicalsimulationdoes not work, chanelextensionmethodcan be used – less intuitive but powerful (implementable as a simplesemi-definiteprogram!) RDD,J. Kolodynski, M. Guta, arXiv:1201.3940 (2012)

  21. Gallery of decoherencemodels • on theboundary, extremal insidethe set of quantum channels fullrank • on theboundary, but non-extremal • on theboundary, non-extremal, • but -extremal, classicalsimulation possible • classicalsimulation • possible channel extensionmethod • channel extensionmethod

More Related