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Chapter 8 Quantum light（第2页）

&herkindsofquantumlightthatprovidedifferentsortsofes。Recallthatlightisossoftheeleagicfield。Alaserbeammostnearlymimicsthisidealbehaviour。Yetevenithassome‘heamplitude。Thatis，eaeasurethefieldamplitude，yougetadifferehesituatioFigure36a，whieuyaboutthefieldateat，orphase，ofitsos。Thereisaparticulartypeofquantumlight—called‘squeezedlight’—forwhioisevarieswiththepointinthecycleofthefield，asshowniisbiggeratsomephasesthaurnsoutthatsuchafieldisposedofonlypairsofphotons。Ifyoumeasuretheons，youwillonlyeverfindanevehequantuminterferehesepairsistheinofthephase-depeudenoise。

&ainthingsyoudowithsuchastate。Imagiyouwaomakeameasurementofthephaseofthewave。（Recallthatthatiswhatyoudoier，andthephaseshiftissomethihelightbeambyayou’dliketomeasure，suchasthepresenceofaparticularmolecule。）Thephasebedeterminedmuchmorepreciselyatpointsiioheflusofthefieldaresmallest。Infact，theflusinthesqueezedlightfieldaresmalleratsomephasesthananyclassicalfield，sothatphasesenssuchafieldwillbemorepresensclassicalfields。Infacttheywillbreakthestandardquantumlimit。

Thisisacostlyapproasi，soitisohereisaclearadvaobehad—forihedeteofgravitywavesbymeanseoptiterferometers，suchastheGEO600projeearHanermany。Byusi，thisidetectphaseshiftsthatdtoarelativepathlengthgeofthelightequivalenttothesizeofanatomparedtothedistaheEarthtotheSun。

36。Squeezedlighta。hasreduoiseiudeatpointsinitsosparedthtb。

Quaa

Thirangerwhenweorethaumlightbeam。Photowinedinsuchawaythatitisimpossibletoascribeapropertytoeitherofthemindividually—forexample，acolour，positioion，orpulseshape。Thisgoeswellbeyondthefuioicleduality。Itgestheverynotionthatintheclassicalworlditispossibletoassignrealvaluesofpropertiestophysitities（e。g。ibeams，sayfrequendtimeofarrival，orH-andV-polarization）—inawaythatberevealedbyalocalmeasurementinaself-tfashiohatthisotbedonefhtbeamspreparediates，andbeprove，isoriumphsoffuithe20thtury。

&hisproperty，itispossibletousequantumopticstoexplorethefamousjectureofEinstein，BorisPodolsky，andNathanRosengwhetheraquantummeicaldesofasystemofpartibesideredplete，requiringnootherinformatioermihingaboutthesystem。JohnBelldisthe1960sameanstoquantifysuchaquestioobuildauallytesthishypothesisbegaheseareknowncolloquiallyas‘Belltests’，aagworkusespairsofphotons，eachofwhichiscorrelatedwiththeother。Itisthehesecorrelationsthatissodifferentforquantumpartiforclassies。It’sworthexplthisinabitmoredepthiafullerserahisqua。

&ionsbefoundiuation。siderforihefollowingsimplegame。Adealertakestwopacksofewithgreenbadtheotherwithbluebacks。Thedealerpieeadgivesooyouaoyourpartner。Eachofyoulooksatyourcard。Theyalwayshavedifferenttheback，ofcourse，buttheymayhavethesamecolour（redorblathefront。Infact，you’dexpectthistooccurhalfthetime，sinceeachofyouwouldexpedividuallytogeteitherredorblackrobability（halfoftheeachdeckarebladhalfred）。

Ifyouandyourparthateverytimeyoubothgotblack，you’dsaythatthecardswere‘correlated’。Thisisabacorrelationasyoue。Infact，ifyoubothgotthesameorethaime，you’dalsobeabletoclaimthecardswerecorrelated，thoughclearlythecorrelationswouldbe‘weaker’thainstahecorrelations，youcoulddetermihedealerwasg，sinightassumeshe’dstartwithtwoi，pletedecks。

Wemakeananalogyofthiskindofcorrelationforphotonsusingpolarizationinsteadofsuitforthecards。Thatis，ahorizontallypolarizedphotoermeda‘red’photoicallypolarizedphotona‘blae。Thenifasourceprodustwoatatime，asdescribedabove，yousaythatitproducescorrelatedphotoalrodusrescribedpolarizatioiehorizontal，orbothhorizontal。Thistypeofed‘classiceithasapleteanalogytothesituationwithclassicalobjectslikeplayingcards。

Thereisafeatureofcorrelationsthathasanintrinsitummeicalaspect。Let’ssaytherearetwopossiblestatesinwhichthephotonpairbeprepared—thefirstH-polarizedandthesedV-polarizedorviceversa。Intheclassicalworldthesetwosituationsfortwoparticlesaremutuallyexclusive:eitherHVorVHispossible，eachrobabilityofone-half。But，justasthesionasuperpositionHandV，sothepair:HVandVH，shownihisturnsouttobeamugercorrelationthanispossiblewithanyclassicalpartidistaisthemostenigmaticpropertyofquantumphysidhasextraordinaryces。

Thesearerevealedbymeas。Insuchatest，youhavetootonlythepossibilityofcorrelationsintheHandVpolarizatioicle，butalsothoseinthediagonal（D）andanti-diagonal（A）polarizations，eatedhalfwaybetweealaical。（Diagonallypht，forexample，isshownii-diagonalpolarizatiorightaheDdire。）Theanalogywiththecardsisthatyoulookatthefrontofthedobserveeitherred（equivalenttoH）orblack（equivalenttoV）suits。OryoucouldlookatthebadseegreetoD）orblue（equivalenttoA）。

37。Alightseingpolarizatioons。

Aquantumgame

Nowimagineacardgameinwhichthedealereitherpadgivesooeachplayer。Thatmeansthateachplayerwillhaveacardthatcouldbeeitherred（R）orblathefront（F）ahergreen（g）orblue（b）ontheback（B）。Thedealerchoosestohandoutsuchawaythatifoneplayerlooksatthefrontofhisdtheotherthebackofhers（F，B），thentheyheresult（R，b）。Similarlyifthefirstplayerlooksatthebackofhisdtheotherthefrontofhers（B，F），thentheyheoute（b，R）。However，whehlookatthefrontoftheircards（F，F）theysometimessee（R，R）。Fromthis，youwouldcludelogicallythatinsuchacase，hadtheylookedatthefrontoftheircards（B，B）theywouldhaveseen（g，g）。That’swhatenforobviouslyclassigslikecards。

38。Tableoftheprobabilitiesofpossibleoutesforaquantumcardgame。

Butinfayoutakephotons（orotherparticles）thatarequaedanddosuexperimeurnoutthatensisthatwhentheplayersmakemeasurementsofthepolarizationsusing，forthefirstplayer，ahorizontallyorientedpolarizer，and，forthesedplayer，adiagonallypolarizedphoton（orviceversa），theyheresults（V=0，D=1）and（D=1，V=0）。Likewise，whehmeasureusingdiagoedpolarizers，theysometimesgettheresult（D=1，D=1）。Thereforeyouwouldlogicludethatwhehephotonsusingahorizontallyorientedpolarizer，theywouldsometimesgettheresult（H=1，H=1）。But，whehisexperiment，theyhisoute!ThetableofpossibleresultsofsutumcardgameareshowninFigure38。Suchexperimentsdhavebeen，doneusingphotonpairs。It’snotfi。

Localpropertiesofthings

Sowhatisgoingon?Thisisthefuallyweirdthingaboutquantumphysics:theofthequantumcardgameisthatthephotonsothavepredetermiheirpolarizatioheyarepreparedatthesource。Itisasifthecardsothavebeeesuitsfromadeckecifiedcard-backcoesagainstallintuitionaboutcards:theysurelyhavedefiiesofaspecifithefrontofeadaspecificthebaatteroreventhedealerknowswhatthesevaluesareordoubtthatthecardsactuallyhavethesepropertieswheous。Aainlydoahemgesthoseproperties。Butquaellsusthatweotassigncolourstothecardsapriori。

Itisthemeasurementsthatgivedefiheoutes。Wethemeasurementssimplyrevealpredetermiiesofthephotons，whiknowntotheplayers。Itisactuallythatyouotassigepolarizationstotheindividualphotoheyareproducedbythesoursuchawayastogivetheoutesthatareactuallyseen。Ifyoutrytodeviseawayofdealingcardsthatgivessucharesult，you’llfindthatitisimpossible。Thecardswouldohavethepossibilitythattheybesimultaneouslyiionsofredandblackreeicularways。Justsothephotons—itisnetobeiionsofHandVinawaythatgivesveryspecifictypesofcorrelations。Itisthistypeofcorrelationthatistermed‘quaa’。

&aisaveryweirdcept。Itisnotpossibletofindawaytothinkaboutitintermsofoneverydayobjects—astheplayingcardexamplewasioshow。Yeteisalsoveryon。Itappearsinmanythiumsineverydays:iioronsinmolecules，givioboomsmakingupthemolecule，oreveivelysmallatomsthemselves，aswellasexoticmaterialslikesuperductors。

Surprisiaurnsouttohaveteplis。You’dhardlythinkthatsuardabstractideacouldpossiblyhaveanyappli，butitdoes。Iteofinformatiapproachesthatotbereplicatedbysendingclassicalwavesbadforth。Iheveryideathatallinformatisystemsareatbottombuiltofsomethithedesignprihesemaesmustreflederlyingphysicsofthetparts—usuallyclassicalphysics。Thishasledtotheuandingthatbasingputing，unieasurementonquantummeicsprovidesueologiesthatsurpassthoseeioninunimaginableways:uniswhuarahelawsofersthatsolve‘unputable’problems;imagirevealaheyarenotevenlookingat。

Lightplaysanimportantpartiingsuchsystems。Theinfrastructureofopticalfibreworks，forinstanbeusedtodistributerandom‘quantumkeys’（randsof0sand1s）pletelysecurelybetweentwoparties，whitheoenessages。Suetworksalsobeusedtoall-stumprocessors，eventuallybeingadistributedquantumputer。Ihasbeenshoriispossibletobuildaquantumputerpletelyoutoflight，thoughitisextremelygtodoso。bieologiesholdsthepromiseiureofaqua，aradicallydifferentwaytounidproatioeologywetlyuse，andallenabledbylight。