Squeezed vacuum as a universal quantum probe.pdf

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1、PhysicsLettersA373(2009)934–939ContentslistsavailableatScienceDirectPhysicsLettersAwww.elsevier.com/locate/plaSqueezedvacuumasauniversalquantumprobeRobertoGaibaa,MatteoG.A.Parisa,b,c,∗aDipartimentodiFisicadell’UniversitàdiMilanoI-20133,ItalybCNISM,UdrMilanoUnive

2、rsità,I-20133Milano,ItalycInstituteforScientificInterchangeFoundation,I-10133Torino,ItalyarticleinfoabstractArticlehistory:WeaddresslocalquantumestimationofbilinearHamiltoniansprobedbyGaussianstates.WeevaluateReceived10December2008therelevantquantumFisherinformat

3、ion(QFI)andderivetheultimateboundonprecision.UponReceivedinrevisedform8January2009maximizingtheQFIwefoundthatsingle-andtwo-modesqueezedvacuumrepresentanoptimalandAccepted19January2009universalclassofprobestates,achievingtheso-calledHeisenberglimittoprecisioninte

4、rmsoftheAvailableonline22January2009overallenergyoftheprobe.WeexplicitlyobtaintheoptimalobservablebasedonthesymmetricCommunicatedbyP.R.HollandlogarithmicderivativeandalsofoundthathomodynedetectionassistedbyBayesiananalysismayachieveestimationofsqueezingwithnear-

5、optimalsensitivityinanyworkingregime.©2009ElsevierB.V.Allrightsreserved.1.IntroductionInthisLetterweaddressquantumestimationofunitaryopera-tionsforcontinuousvariablesystems.InparticularweanalyzetheFig.1.GeneralschemefortheindirectestimationoftheunitaryUθprobedby

6、theestimationoftheinteractionparameterθforunitariesoftheformsignal0.Uθ=exp(−iθG)whereGisalinearorbilinearbosonicHamilto-nianoftheformG=a†b+ab†,G=a†b†+ab,orG=a†2+a2,[a,a†]=1and[b,b†]=1beingmodeoperators.Weareinterestedi.e.apositiveoperator-valuedmeasure(POVM){Ex

7、}x∈X,tobeper-†inevaluatingtheultimateboundonprecision(sensitivity),i.e.theformedontheprobeθ=Uθ0Uθaftertheinteraction,atfixedsmallestvalueoftheparameterthatcanbediscriminated,andtoenergyN=Tr[0jnj]oftheincomingsignal,jnjbeingthedeterminetheoptimalmeasurementac

8、hievingthosebounds.totalnumberoperatoroftheinvolvedmodes.Asamatteroffact,linearandbilinearinteractionsforbosonicTheaboveproblemmaybeproperlyaddressedintheframe-system