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1、QuantumstatessatisfyingclassicalprobabilityconstraintsElenaR.LoubenetsAppliedMathematicsDepartment,MoscowStateInstituteofElectronicsandMathematicsFebruary1,2008AbstractForlinearcombinationsofquantumproductaveragesinanarbitrarybipartitestate,wederivenewquantumBell-formandCHSH-f
2、orminequalitieswiththeright-handsidesex-pressedintermsofabipartitestate.ThisallowsustospecifyinageneralsettingbipartitestatepropertiessufficientforthevalidityofaclassicalCHSH-forminequalityandtheperfectcorrelationformoftheoriginalBellinequalityforanyboundedquantumobservables.Wea
3、lsointroduceanewgeneralconditiononabipartitestateandquantumobservablessufficientforthevalidityoftheoriginalBellinequality,initsperfectcorrelationoranticorrelationforms.Underthisgeneralsufficientcondition,abipartitequantumstatedoesnotnecessarilyexhibitperfectcorrelationsoranticorre
4、lations.Contents1Introduction12Quantumupperbounds.Generalcase22.1Source-operatorsforabipartitestate..........................32.1.1ExamplesofDSOandBellclassstates.....................42.2QuantumBell-forminequalities.............................62.3QuantumCHSH-forminequalities.
5、..........................8arXiv:quant-ph/0406139v230Mar20053ValidityofclassicalBell-typeinequalitiesinthequantumcase83.1GeneralizedquantummeasurementsofAliceandBob................111IntroductionTheBell[1]andtheClauser-Horne-Shimony-Holt(CHSH)[2]inequalities,derivedoriginallyi
6、ntheframeoftheBelllocalhiddenvariablemodel,describetherelationsbetweentheproductexpectationvaluesunderdifferentjointmeasurements.Intheframeofclassicalprobability,foranyboundedclassicalobservables,theproductexpecta-tionvaluesineveryclassicalstatesatisfytheoriginalCHSHinequalitya
7、ndtheperfectcorrelationformoftheoriginalBellinequality1.Intheframeofquantumprobabilityand,moregenerally,quantummeasurementtheory,theproductexpectationvaluesunderjointquantummeasurementsonabipartitesystem,donot,ingeneral,satisfyaBell-typeinequality.Itis,however,wellknown[4,5]th
8、atthereexistnonseparablebipartitestatesthatsatisfytheCHSHineq
