Lecture Notes for Physics 229 Quantum Information and Computation

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1、LectureNotesforPhysics229:QuantumInformationandComputationJohnPreskillCaliforniaInstituteofTechnologySeptember,19982Contents1IntroductionandOverview71.1Physicsofinformation......................71.2Quantuminformation.......................101.3Ecientquantumalg

2、orithms..................111.4Quantumcomplexity.......................121.5Quantumparallelism.......................161.6Anewclassicationofcomplexity................191.7Whatabouterrors?........................211.8Quantumerror-correctingcodes.................

3、261.9Quantumhardware........................301.9.1IonTrap..........................311.9.2CavityQED........................331.9.3NMR............................341.10Summary.............................362FoundationsI:StatesandEnsembles372.1Axiomsofquantummec

4、hanics..................372.2TheQubit.............................4012.2.1Spin-...........................4122.2.2Photonpolarizations...................482.3Thedensitymatrix........................492.3.1Thebipartitequantumsystem..............492.3.2Blochsphere

5、........................542.3.3Gleason'stheorem....................562.3.4Evolutionofthedensityoperator............582.4Schmidtdecomposition......................592.4.1Entanglement.......................612.5Ambiguityoftheensembleinterpretation............6234

6、CONTENTS2.5.1Convexity.........................622.5.2Ensemblepreparation...................642.5.3Fasterthanlight?.....................662.5.4Quantumerasure.....................682.5.5TheGHJWtheorem...................712.6Summary.............................73

7、2.7Exercises..............................753MeasurementandEvolution773.1OrthogonalMeasurementandBeyond..............773.1.1OrthogonalMeasurements................773.1.2Generalizedmeasurement................813.1.3One-qubitPOVM.....................833.1.4Neumar

8、k'stheorem....................843.1.5Orthogonalmeasurementonatensorproduct.....863.1.6GHJWwithPOVM's...................913.2Superoperators..........................923.2.1Th