苏汝铿高等量子力学讲义(英文版)Chapter7 Quantum Enta.ppt

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1、Chapter7QuantumEntanglementandQuantumInformation§7.1PurestatesandmixedstatesIntroduction:Quantumentanglementdescribesthecoherenceoftwoormanyquantumstatesaccordingtothesuperpositionprincipleofquantumstates.Energy:interactions,conservationlaws,work…Entropy:information,orderanddisorder…Entanglement:c

2、oherence,teleportation…Purestate§7.1PurestatesandmixedstatesSystemA:SystemsA+B:Purestate§7.1PurestatesandmixedstatesDensitymatrix:InthebaseoftherepresentationO§7.1PurestatesandmixedstatesTheaveragevalueofaquantityF:§7.1PurestatesandmixedstatesMixedstate:thenon-coherentmixtureoftwoormanypurestatesSy

3、stemA:§7.1PurestatesandmixedstatesInthebaseoftherepresentationO§7.1PurestatesandmixedstatesSystemsA+B:thereduceddensitymatrixIfisaobservablequantityofsystemA,itsaveragevalue:isaunitoperatorofsystemB.§7.1Purestatesandmixedstatesiscalledthereduceddensitymatrix.§7.1PurestatesandmixedstatesThepropertie

4、sofmeasurement§7.1PurestatesandmixedstatesForas=1/2particle:PureState:MixedState:Thesuperpositionstateanditsmixedstate:§7.1PurestatesandmixedstatesThemeasurementof:PureState:MixedState:§7.1PurestatesandmixedstatesThemeasurementquanityPurestateMixedstate§7.2EntangledstatesandBellbasisEntangledstate:

5、non-entangledstate:Schmittheorem:Atwoparticlespurestatecanbeexpressedas§7.2EntangledstatesandBellbasisProve:aretheorthogonalbasisofhillbertspace.§7.2EntangledstatesandBellbasis§7.2EntangledstatesandBellbasisBellbasis:§7.2EntangledstatesandBellbasisThedensitymatrixofparticleAforthestate:Mixedstate.§

6、7.2EntangledstatesandBellbasisForthestate:Mixedstate.Forthenon-entangledstate:Purestate.§7.2EntangledstatesandBellbasisWecanmaketwonewentangledstates:Bellbasis:§7.2EntangledstatesandBellbasisThereforeBellbasisarethecommoneigenstatesof§7.3SchordingercatandwhichwayexperimentsSchordingercatrecentexper

7、imentsWhichwayexperiments§7.3Schordingercatandwhichwayexperiments§7.3Schordingercatandwhichwayexperiments§7.3Schordingercatandwhichwayexperiments§7.4MeasurementanddecoherenceMeasurementWavepacketcollapseQua