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&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
ThirangerwhenweorethaumlightbeaPhotowinedinsuchawaythatitisimpossibletoascribeapropertytoeitherofthemindividually—forexample，acolour，positioion，orpulseshape.Thisgoeswellbeyondthefuioicleduality.Itgestheverynotionthatintheclassicalworlditispossibletoassignrealvaluesofpropertiestophysitities（e.g.ibeams，sayfrequendtimeofarrival，orH-andV-polarization）—inawaythatberevealedbyalocalmeasurementinaself-tfashiohatthisotbedonefhtbeamspreparediates，andbeprove，isoriumphsoffuithe20thtury.
&hisproperty，itispossibletousequantumopticstoexplorethefamousjectureofEinstein，BorisPodolsky，andNathanRosengwhetheraquantummeicaldesofasystemofpartibesideredplete，requiringnootherinformatioermihingaboutthesysteJohnBelldisthe1960sameanstoquantifysuchaquestioobuildauallytesthishypothesisbegaheseareknowncolloquiallyas‘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.
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