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Bell inequality. Bell Inequality in Particle physics. The Feasibility of Testing LHVTs in Charm factory.2x AhA2 B 0  0 0  0 1.EPR-B paradoxaIn a complete theory there is an element corresponding to each element of reality. Physical reality: possibility of predicting it with certainty, without disturbing the system. Non-commuting operators are mutually incompatible. I. The quantities correspond to non-commuting operators can not have simultaneously reality. or II. QM is incomplete. VbA1EfE7AFA ,EPR: ( Bohm s version)0B$$B$  Bohr s reply $Bohr contest not the EPR demonstration but the premises. An element of reality is associated with a concretely performed act of measurement. This makes the reality depend upon the process of measurement carried out on the first system.A 2.Bell Inequality (BI)EPR-(B)Z #Hidden variable and Bell inequality$$.Optical experiment and result$ +%3.Bell Inequality in Particle physicsTest BI with fermions or massive particles. Test BI with interactions other than electromagnetic interactions. Strong or Weak actions. Energy scale of photon case is eV range. Nonlocal effects may well become apparent at length scale about cm.A,E% $ Bell Inequality in Particle physics %$B!In spin system: the measurement of spin correlation in low-energy proton proton scattering. [M.Lamehi-Rachti,W.Mitting,PRD,14,2543,1976]. Spin singlet state particle decay to two spin one half particles. [N.A. Tornqvist. Found.Phys.,11,171,1981]. With meson system: Quasi spin system.A B&   '  ;Other form of nonlocality  Nonlocality without using inequalities. GHZ states: three spin half particles.(1990) Kochen-Specher: two spin one particles.(80) L. Hardy: two spin one half particles. f((C &AC'AC(A, JE"&GHZ states: three spin half particles.$'%C A #'Kochen-Specher: two spin one particles.((C  $&L. Hardy: two spin one half particles.''C  %  )/Hardy type experiment with entangled Kaon pairs00 %rGenerate a asymmetric state. Eberhard s inequality (EI). ::A" '  (  /34.The Feasibility of Testing LHVTs in Charm factory44(xEasy to get space-like separation. Can test the phenomena: less entangled state leads to larger violation of inequality.yyAL  _1  w  `The advantage of over  ( Quantify the entanglement a  .The Entanglement and Bell inequality violation//  5     0` 3333ff3` 3333f33ff3` "3333̙ff3` Kf3̙` &e̙3g3f` f333̙po7` ___f3̙;/f9` ff3Lm` ff3LmNLm>?" dd@*?nAd@q<nAqFLK#M n?" dd@   @@``PR    M`2p>> lx(  l l HY? ?" `}  LUSQdkYkHrh7h_  " l H|\? ?" `  8USQdkYkHre,g7h_ ,{N~ ,{ N~ ,{V~ ,{N~   l 6b #" `] `}  Z*  l 6i #" ``   \*  l 6k #" `] `}  \*  l C @ABCDE FjJ@3"0`B l s *DjJ"0 `0H l 0޽h ? ___f3̙;/f9___PPT10i.  +D='  = @B + Edge T 0 pv(  p p H-? ?"@   LUSQdkYkHrh7h_   p H( ? ?"   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Due to angular momentum conservation and Einstein s argument of reality and locality, the quantities of Non-commuting operators of the second particle can be simultaneously reality.,0Cx  c $0l9M     <d  , QSo QM is incomplete ! 0CH  0޽h ? ___f3̙;/f9___PPT10i.b0\+D='  = @B + T 0 pC(  r  S l `}   r  S l `     < &  >0 e  04p   aThat it is the theory which decides what is observable, not the other way around. ----Einstein b0gfgf;gfCH  0޽h ? ___f3̙;/f9___PPT10i. +D='  = @B + T 0  o(  ~  s *8Ul'g  U ~  s *tUln U   <L FHidden variable theoryQ  0"Uwl  Von Neuman (1932) : the hidden variable is unlikely to be true. Gleason(1957), Jauch(1963) , Kochen-Specher(1967) D>=3 paradox. 2[$x  <U u  4Bell   0(U6 t"  `D=2. Bell inequality(1964). D>=3. contextual dependent hidden variable theorem would survive. aaX  0X   0cX   0s 7 Xr   0'% H  0޽h ? 33___PPT10i. +D='  = @B +  T 0 #   (  ~  s *8Ul `  U  0  `A ? ?l"`W  U 0  `A ? ?l"` 9   URB  s *DFfRB  s *DFF  <=UF n a   <@Ug+ b   <,DUw3 cRB   s *DFPRB   s *D]FI   <HU d 0 TA ? ?l}W  U  0 ?? ZC  K  <U ?"6@ NNN?Nc 6Y  W. Tittel, et al D nA CCC H  0޽h ? ___f3̙;/f9___PPT10i.Mš+D='  = @B + T 0 (  r  S ܞUl `}  U r  S Ul ` U `  c $A A??F x]  A  <LU 1  #S.A. Abel et al. PLB 280,304 (1992)B$0   H  0޽h ? ___f3̙;/f9___PPT10i.`z+D=' U= @B + T 0 <(  ~  s *`Ul `}  U ~  s *8Ul `v U H  0޽h ? 33___PPT10i.мV+D=' U= @B +$ T 0 ;3(  `  c $A ??r `  c $A ??, d  x  <Ab i ??P i x  <A ??0  x  <A ??e0 ;   <oU,Yu bMass eigenstates   <U, ~ `CP eigenstates    <UZA _ S eigenstates `   c $A ??w) x   <A ??w    <U  TLike the photon case they don t commutate "+)A`   c $A ??B p x  <A  ?? 0 m   x  <A !??7  !  <   "H   0޽h ? ___f3̙;/f9___PPT10i.Pf\+D=' U= @B + T 0 / ' 00  (  r  S l `j  E  8 2  2 n  s *AW O??2h On  s *AS ??r 2E n  s *AR ??$  n  s *AQ ??q   =   HE  ?"6@ NNN?Nc u   7But because of 2 & 3. If D=1 then G=1. If E=1 then F=1.&8 nA8C   HE  ?"6@ NNN?N / So if the probability that D=E=1 is not 0, then the probability for F=G=1 won t be 0.<V nAJC G,   HE  ?"6@ NNN?N  v&Jordan proved that for the state like:&' nA'C^   H@ f  ?"6@ NNN?Njq  PRA50, 62 (1994) Jordan f nAAAAA AC`  c $AP ??Zm `  c $AN ??f   HLf  ?"6@ NNN?Nu RIf& nAC  Hpf  ?"6@ NNN?N]F} Z& nAC 4  H*f  ?"6@ NNN?N: ~.there exist four projection operators satisfy:&/ nA/CH  0޽h ? ___f3̙;/f9___PPT10i.2+D=' U= @B + T 0 @#P0 (  Z8   J%  n  s *AO M??  M!  Z0f GH  ?"0 NNN?N` C W1,(nAE! ! Z9f GH  ?"0 NNN?NfC W2,(nAE! " Z HD?"0@NNN?N M B ? HD?"0@NNN?NMB @ BD?"0@NNN?N MMF  [ B mh C c $AV ?? [ ~T z  D#  B E HD?"0@NNN?NB F BD?"0@NNN?Nz B G HD?"0@NNN?Nz z  H H?"0@NNN?N } 8   P= 5 L Tnf  ?"6@ NNN?N #  kConsider the CH inequality:& nACC M Tof  ?"6@ NNN?N#  yPRD10, 526 (1974)> nAAA Av N Tf  ?"6@ NNN?Nv PRA52, 2535 (1995) Garuccio L nAAAAC? O Tf  ?"6@ NNN?Nr Z  }Eberhard Inequality& nAC H  0޽h ?_`  !"#H ___f3̙;/f9___PPT10i.ľ[Fn+D=' U= @B + T 0  (  x  c $f l9  f  x  c $xf l9 f  `  c $A D??  D`  c $A f?? T&  f8      <Жf    gPRL88, 040403 (2002),60AAA   0؞f    gPRL89, 160401 (2002).60AAA   <f  6 JQuant-ph/05011069.0Ad  Hȭf  ?"6@ NNN?N "  A. Bramon, and G. Garbarino:$ nAA4   Y  Nf  ?"6@ NNN?N + )A. Bramon, R. Escribano and G. Garbarino:$* nA*A) H  0޽h ? ___f3̙;/f9___PPT10i.Ĩw+D=' U= @B +Z T 0 qi` (   `   c $A^ )??   )   H\f  ?"6@ NNN?ND-| } To generate the asymmetric state, fix a thin regenerator on the right beam close to decay points. Then the initial state:4~ nACzC`   c $A] '?? '   TPf  ?"6@ NNN?N 2Z  XBecomes:& nA C>   Txf  ?"6@ NNN?N q# |,Let this state propagate to a proper time T:&- nA-CH   0޽h ? ___f3̙;/f9___PPT10i.;@l+D=' U= @B +] T 0 tlp $(  $? $ Tf  ?"6@ NNN?N C(  }-Normalize it to the surviving pairs leads to:&. nA.C` $ c $A\ %??F W  %yF z G< $ S z Gh $ c $A[ &?? G, & $ <pf z  < ?where0C`  $ c $AZ *??W *.  $ Tf  ?"6@ NNN?N}h  lcomponent has been enhanced.& nAC.  $ Tv  ?"6@ NNN?NC c  lhas been further suppressed.& nAC`  $ c $AU +??}Tt +`  $ c $A_ .??:Ttw  .H $ 0޽h ? ___f3̙;/f9___PPT10i.=S+D=' U= @B +h T 0 w (  r  S 5l `}   r  S `6l `  `  c $AE ?? ~  `  c $A: ??S  <    <l8  p6In the charm factory the entanglement state formed as:707Cf  s *A! ??f k    B=   ?where0CH  0޽h ? ___f3̙;/f9___PPT10i.0jS+D=' U= @B +  T 0 $ (  `  c $A/ ??]  `  c $A+ ??} g  `  c $A, ??a d0  `  c $A. ??) V     0f 'C rThe four joint measurement of the transition probability needed in the EI predicted by QM take the following form:s0sC`   c $A ??, d  `  c $A ?? ` H  0޽h ? ___f3̙;/f9___PPT10i.;+D=' U= @B + T 0   0 ? (  x  <A r?? *  r  BT'8V G Take into EI:0Cf   s *A- ??/    <pv  zw  @ See Figure 1 0 8 wLT Km S n   s *A;  ??wjT  n  s *A% ?? cO M   Bv =L F >(for0C  B$ LF H See figure 3)0C  <v  ?"6@ NNN?N0 - dwhere 4 nACC`  c $A6 ??" @  0  H)v  ?"6@ NNN?N"T  z*is the violation degree of the inequality.&+ nA+C  H8v  ?"6@ NNN?N*v  Z& nAC   HBv  ?"6@ NNN?NCTc  `From QM we have:& nAC  HLv  ?"6@ NNN?NYK S  \ First assume& nA C 0 TA0 6 ? ?l W \ 6   0 0 v H  0޽h ? ___f3̙;/f9___PPT10i.ϐ+D=' U= @B +3 T 0 JB@ (     S 2A&violationw@  0 0H  0޽h ? ___f3̙;/f9___PPT10i.8[$+D=' U= @B +e T 0 |t`  (    <Ov '  a'Actually has non-zero magnitude :(0(CL  C $A  phaseeC   0Tv   The shaded region is the requirement of the real and imagine part of R when violation between QM and LHVTs can be seen from inequality.0Ce`   c $A@ ??&  H  0޽h ? ___f3̙;/f9___PPT10i.5D+D=' U= @B + T 0 )N(  x  c $\v l `}  v  f  s *A< "??}=n  "f  s *A= +?? <m  +f   s *A( ??g    B`v  ;factory0f   s *A) ?? *     Bbv    A Charm factory0   <fv XT, R [Space-like separation required: 0 C`  c $A3 ??, n `  c $A9 ??:< `  c $A? ??` !  `  c $A$  ??  n   `  c $AC ??P    < t` 6In0  6pv T VTo make sure the misidentification of is of order per thousandW0WC`  c $AA ??@ t `  c $A7 )??/- 9 )  <tv .T( JProperly choose0C  <yv /I fPRL88, 040403 (2002)60AAA`  c $A" ?? P m  `  c $AB ??*J  `   c $A8 }?? V  } ! <v  6so0 " <̀v F -  6so0? ' Ḧv  ?"6@ NNN?N W  9 has a wider region of R in discriminating QM from LHVT.&: nA:C` ( c $A) U??   UL ) Hv  ?"6@ NNN?N '  6There is phenomena can be test due to this advantage. 67 nA5CCH  0޽h ? ___f3̙;/f9___PPT10i.`u+D=' U= @B +  T 0     (  r  S Dv l `}  v  `  c $A2 ?? 6    <v c _J  FPRL80, 2245 (1998)0  <hv c P J  a W. Wootters 0 `  c $A*  ?? }     <pv 6 S0  @Where:0C@   <v ] G@  0 0 @This mean the state become less entangled during time evolution!0A0?CC   <v  ?"6@ NNN?NG9 Historically the amount of the violation was seen as extent of entanglement. This may not be the case in EI. As indicated in Figure 1 & 2.( nACT  <v  ?"6@ NNN?N&Y 8To see this we must quantify the degree of entanglement H9 nA7CCC7  HPv  ?"6@ NNN?N% /Take concurrence as a measure of this quantity.(0 nA0CI  H v  ?"6@ NNN?N   CC changes between 0 to 1 for no entanglement and full entanglement.&D nADCH  0޽h ? ___f3̙;/f9___PPT10i.è#+D=' U= @B +  T 0   W (    6A ? ?#" `/ `  c $A' &?? &  0v ,'s /Express the violation in degree of entanglementN00   BX+D=' U= @B +B T 0 YQ t(  tr t S +l `}    t 0D c }5Magnitudes below zero of VD is the range of violation,60 +R  t C *ADbreaking'cH t 0޽h ? ___f3̙;/f9___PPT10i.+D=' U= @B +R T 0 ia(   @ 0, P a+ Thank you for your patience. ,0,&H  0޽h ? ___f3̙;/f9___PPT10i.<<+D=' U= @B +"xXMlE~3vcv@[ 8 I6Hq$- ֚?{ݠPH{TzBPp潝]qf4@}};μ??uh Aw5>jVk(ا! wU7e1<_w+NBMa68#lɌ=;e*C4\y !2ްUAkb^ldb0 }kv^_#w3Vl7mIl ݇}8pʧ-%\ ꀕ=ػU( )c)(]ytNPO7pA+S@5Al7aSkvdUYXu1g_ab&@6ܻYw7Ro_d}40%泟}u&? 9-K%JRQnjjb NO<tsv1A/MO*..N3XRLJLԬ^3pz& NZt>Mqh$K4 B@ oeӚ5S$+K*sT]=+~߳%#wÕj~ujHdhX/F )6q\!,^ e[ QΑ  >ͳ:ahOcR:| _9BcnFEkL~Kwwt>dBcE|x<)B(N(y !NZ/g~*]9tT<݄?yȍG> veY d!A3223z/ ֢6-"ge9~K7kVawzobˌz+pix:OpGU/uvoFh1]|Nִc%_/TbV$:cΩx*8ww7wjWwoy ;w_5m ]{-kzq*m$xX]lTUs.B, P McMH,R." 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Bell inequality. Bell Inequality in Particle physics. The Feasibility of Testing LHVTs in Charm factory.2x AhA2 B 0  0 0  0 1.EPR-B paradoxaIn a complete theory there is an element corresponding to each element of reality. Physical reality: possibility of predicting it with certainty, without disturbing the system. Non-commuting operators are mutually incompatible. I. The quantities correspond to non-commuting operators can not have simultaneously reality. or II. QM is incomplete. VbA1EfE7AFA ,EPR: ( Bohm s version)0B$$B$  Bohr s reply $Bohr contest not the EPR demonstration but the premises. An element of reality is associated with a concretely performed act of measurement. This makes the reality depend upon the process of measurement carried out on the first system.A 2.Bell Inequality (BI)EPR-(B)Z #Hidden variable and Bell inequality$$.Optical experiment and result$ +%3.Bell Inequality in Particle physicsTest BI with fermions or massive particles. 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Bell inequality. Bell Inequality in Particle physics. The Feasibility of Testing LHVTs in Charm factory.2x AhA2 B 0  0 0  0 1.EPR-B paradoxaIn a complete theory there is an element corresponding to each element of reality. Physical reality: possibility of predicting it with certainty, without disturbing the system. Non-commuting operators are mutually incompatible. I. The quantities correspond to non-commuting operators can not have simultaneously reality. or II. QM is incomplete. VbA1EfE7AFA ,EPR: ( Bohm s version)0B$$B$  Bohr s reply $Bohr contest not the EPR demonstration but the premises. An element of reality is associated with a concretely performed act of measurement. This makes the reality depend upon the process of measurement carried out on the first system.A 2.Bell Inequality (BI)EPR-(B)Z #Hidden variable and Bell inequality$$.Optical experiment and result$ +%3.Bell Inequality in Particle physicsTest BI with fermions or massive particles. 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