Deconstructing Dense Coding

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1、DeconstructingDenseCodingN.DavidMerminLaboratoryofAtomicandSolidStatePhysics,CornellUniversity,Ithaca,NY14853-2501Theremarkabletransmissionoftwobitsofinformationviaasinglequbitentangledwithanotheratthedestination,ispresentedasanexpansionoftheunremarkableclassic

2、alcircuitthattransmitsthebitswithtwodirectqubit-qubitcouplingsbetweensourceanddestination.PACSnumbers:03.67.Hk,03.67.LxQuantumdensecoding[1]enablesAlicetocommuni-catetwobitsofclassicalinformationbysendingBobasinglephysicalqubit,whichismaximallyentangledwith=ano

3、therqubitalreadyinhispossession.ShedoestheXHZHtrickbyapplyingoneoffourunitarytransformationstohermemberoftheentangledpair,therebyconvertingXXthestateofthepairintooneoffourmutuallyorthogonal(a)(b)two-qubitstates.Bobcanlearnwhichstateitisafterreceivingthesecondme

4、mberofthepair.WhatissurprisingisthatAliceappearstoactononlyasinglequbit,therebyprovidingBobwithtwobitsofinformationbysendinghimonlyoneappropriatelypre-=paredqubit.ButthiswayoftellingthetaledownplaysHZHasecondinteractionthattakesplacebeforethecurtainXXXevenrises

5、ontheofficialstory.Thatearlierinteractionis(c)requiredtocreatetheentanglementbetweenthequbitsthatAliceandBobinitiallyshare.Thefullstoryremainssurprisingevenwiththisaddedprologue,buttherealsurpriseisthattheentanglingin-teraction,essentialforthetransmissionofthetwo

6、bits,=cantakeplacebeforeAlicehasevenchosenthebitssheHZHwishestocommunicatetoBob.WhatthestoryreallydemonstratesistheremarkableabilityofentangledstatesXXXtostoreinteractioninahighlyfungibleformthatneed(d)notbecashedinuntiltheneedarises.Ihavemadeasimilarpoint[2]ab

7、outquantumtele-portation,showingexplicitlyhowthemissinginteractionthatmakesthedifferencebetweenaroutineclassicalcir-cuitandaquantum“miracle”,isburiedintheinterac-=arXiv:quant-ph/0204107v223Apr2002tionthatproducesacrucialsharedentangledpairbeforeHXXZHthestatetobe

8、teleportedneedevenhavebeenformed.XXBecauseteleportationanddensecodingbothexploitpre-(e)existingsharedentanglementtofacilitatecommunicationwithsurprisinglylittleadditionalint