Dynamical Aspects of Information Storage in Quantum-Mechanical Systems

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1、NORTHWESTERNUNIVERSITYDynamicalAspectsofInformationStorageinQuantum-MechanicalSystemsADISSERTATIONSUBMITTEDTOTHEGRADUATESCHOOLINPARTIALFULFILLMENTOFTHEREQUIREMENTSforthedegreeDOCTOROFPHILOSOPHYFieldofElectricalandComputerEngineeringarXiv:quant-ph/0207162v22Apr2003ByMaximRa

2、ginskyEVANSTON,ILLINOISJune2002cCopyrightbyRaginsky,Maxim2002AllRightsReservediiABSTRACTDynamicalAspectsofInformationStorageinQuantum-MechanicalSystemsMaximRaginskyWestudyinformationstorageinnoisyquantumregistersandcomputersusingthemethodsofstatisticaldynamics.Wedevelopthe

3、conceptofastrictlycontractivequantumchannelinordertoconstructmathematicalmodelsofphysicallyrealizable,i.e.,nonideal,quantumregistersandcomputers.Strictlycontractivechannelsaresimpleenough,yetexhibitveryinterestingfeatures,whicharemeaningfulfromthephysicalpointofview.Inpart

4、icular,theyallowustoincorporatethecrucialassumptionoffiniteprecisionofallexperimentallyrealizableoperations.Strictcontractivityalsohelpsusgaininsightintothethermodynamicsofnoisyquantumevolutions(approachtoequilibrium).Ourinvesti-gationintothermodynamicsfocusesontheentropy-e

5、nergybalanceinquantumregistersandcomputersundertheinfluenceofstrictlycontractivenoise.Usingentropy-energymethods,weareabletoappraisethethermodynamicalresourcesneededtomaintainre-liableoperationofthecomputer.Wealsoobtainestimatesofthelargesttolerableerrorrate.Finally,weexplo

6、rethepossibilityofgoingbeyondthestandardcircuitmodeloferrorcorrection,namelyconstructingquantummemorydevicesonthebasisofinteractingparticlesystemsatlowtemperatures.iiiAcknowledgmentsFollowingthehallowedtradition,firstIwouldliketothankmythesisadvisorandmentor,Prof.HoraceP.Yu

7、en,whonotonlyprofoundlyinfluencedmythinkingandthecourseofmycareerasagraduatestudent,butalsoimpresseduponmethisveryimportantlesson:inscientificresearch,oneshouldneverblindlydeferto“authority,”butratherworkeverythingoutforoneself.NextIwouldliketothankProfs.PremKumarandSelimM.S

8、hahriarforservingonmyfinalexaminationcommittee,Dr.GiacomoM.D’Ariano(UniversityofPavia,Ital