文档介绍：Part2:IndirectinteractionsWeassumethattwoquantumobjectsAandCinteractonlyviaanotherobject(orobjects):Thegroundstateofallsuchsystemscanonlyhavelargeamountsofcorrelation(andthusentanglement)betweenAandCifthereisasmallenergygap(betweengroundandfirst-excitedstates).Specifically,weexpressthegroundstate,withoutlossofgenerality,as::Thentheenergygapandcorrelationsarethenrelatedasfollows:Part1:Two-localinteractionsInnature,many-bodyinteractionstendtobe“two-local”,thatistheyarethesumoftwo-?Consider:?Ninteractingquantumsystems,eachd-level.?Interactionsmayonlybeone-andtwo-,theHamiltonianisasumofoperatorsthateachactonatmosttwobodies:(nontrivial)two-localHamiltonian?Result:Instatespace,centredaroundeverynondegeneratequantumerror-correctingcodestate,isaregionofstatesthancannotbethegroundstateofanyphysically-,correlations,anderror-correctioninthegroundstatesofmany-bodysystemsSummaryArethereanygenericpropertieswhicharesharedbythegroundstatesofallphysically-realisticmany-bodyquantumsystems?Weconsidertwoverysimplenotionsof“physicallyrealistic”.Firstisthatinteractionsbetweenbodiescanbeexpr