holevo,probabilistic and statistical aspects of quantum theory

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1、1QUADERNIMONOGRAPHSAlexanderHolevoSteklovMathematicalInstituteMoscowProbabilisticandStatisticalAspectsofQuantumTheoryAlexanderHolevoProbabilisticandStatisticalAspectsofQuantumTheoryc2011ScuolaNormaleSuperiorePisaISBN:978-88-7642-375-8ContentsForewordtothesecondEnglisheditionixP

2、refacetothesecondRussianeditionxiPrefacexiii1Statisticalmodels11.1Statesandmeasurements.................11.2Somefactsaboutconvexsets...............51.3Denitionofastatisticalmodel..............121.4Theclassicalstatisticalmodel..............131.5Reductionofstatisticalmodel.Classi

3、calmodelwitharestrictedclassofmeasurements.............181.6Thestatisticalmodelofquantummechanics.......231.7Ontheproblemof“hiddenvariables”..........291.8Comments.........................342Mathematicsofquantumtheory372.1OperatorsinaHilbertspace...............372.2Quantumstates

4、andmeasurements............432.3Spectralrepresentationofboundedoperators.......452.4Spectralrepresentationofunboundedoperators.....492.5Onrealizationofmeasurement..............552.6Uncertaintyrelationsandcompatibility..........592.7Trace-classoperatorsandHilbert-Schmidtoperators

5、...632.8L2spacesassociatedwithaquantumstate.......692.9Uncertaintyrelationsformeasurementswithnitesec-ondmoments.......................742.10Matrixrepresentationofsquare-summableoperators.Thecommutationoperatorofastate.............772.11Comments.........................81viAlex

6、anderHolevo3Symmetrygroupsinquantummechanics853.1StatisticalmodelandGalileanrelativity.........853.2One-parametershiftgroupsanduncertaintyrelations..893.3Kinematicsofaquantumparticleinonedimension...933.4Uniquenesstheorem.TheSchrodingerandthe¨momentumrepresentations.............

7、...973.5Minimum-uncertaintystates.Thecompletenessrelation.1003.6Jointmeasurementsofcoordinateandvelocity......1033.7Dynamicsofaquantumparticleinonedimension....1083.8Timeobservable.The“time-energy”uncertaintyrelation1123.9Quantumoscillatorandphasemeasurement.......1173.10Thecohe

8、rent-staterepresentation.............1223.11Rep