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The Feasibility of Testing LHVTs in High Energy Physics

The Feasibility of Testing LHVTs in High Energy Physics. 李军利. Phys.Rev. D74,076003, (2006). 中国科学院 研究生院. In corporation with 乔从丰 教授. 桂林 2006.10.27-11.01. Content. EPR-B paradox . Bell inequality. Bell Inequality in Particle physics.

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The Feasibility of Testing LHVTs in High Energy Physics

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  1. The Feasibility of Testing LHVTs in High Energy Physics 李军利 Phys.Rev. D74,076003, (2006) 中国科学院 研究生院 In corporation with 乔从丰 教授 桂林 2006.10.27-11.01

  2. Content • EPR-B paradox. • Bell inequality. • Bell Inequality in Particle physics. • The Feasibility of Testing LHVTs in Charm factory.

  3. 1.EPR-B paradox • In 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 operatorscan not have simultaneously reality. or II. QM is incomplete. Einstein, Podolsky, Rosen. 1935

  4. EPR: ( Bohm’s version) Two different measurements may performe upon the first particle. 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. So QM is incomplete !

  5. 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. That it is the theory which decides what is observable, not the other way around. ----Einstein

  6. 2.Bell Inequality (BI) Hidden variable theory EPR-(B) Von Neuman (1932) : the hidden variable is unlikely to be true. Gleason(1957), Jauch(1963) , Kochen-Specher(1967) D>=3 paradox. Bell D=2. Bell inequality(1964). D>=3. contextual dependent hidden variable theorem would survive.

  7. Hidden variable and Bell inequality a b c LHVT: d QM: Bell, physics I,195-200, 1964 CHSH, PRL23,880(1969)

  8. Optical experiment and result Aspect 1982 two channel polarizer. PRL49,91(1982) Experiment with pairs of photons produced with PDC W. Tittel, et al PRL81,3563(1998) All these experiments conform the QM!

  9. 3.Bell Inequality in Particle physics • Test 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. S.A. Abel et al. PLB 280,304 (1992)

  10. Bell Inequality in Particle physics • 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.

  11. Mass eigenstates CP eigenstates S eigenstates 1 Like the photon case they don’t commutate Are regard as the quasi-spin states. 2 Note that the H is not a observable [not hermitian] Berltamann, Quant-ph/0410028 Fix the quasi-spin and free in time.

  12. They use to test the BI: Experiment of system A.Go. J.Mod.Opt.51,991. as the flavor tag. However, debates on whether it is a genuine test of LHVTs or not is still ongoing. R.A. Bertlmann PLA332,355,(2004)

  13. 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. Dimension-6 Hardy’s proof relies on a certain lack of symmetry of the entangled state. PRL71, 1665 (1993)

  14. (1) (2) (3) (4) GHZ states: three spin half particles. which contradict (4). “No reasonable definition of reality could be expected to permit this.”

  15. Kochen-Specher: two spin one particles. (1). Any orthogonal frame (x, y, z), 0 happens exactly once. (2). Any orthogonal pair (d, d’), 0 happens at most once. A set of eight directions represented in following graph: If h(a0)=h(a7)=0, then h(a1)=h(a2)=h(a3)=h(a4)=1. So that h(a5)=h(a6)=0, by (1), which contradict (2). Consider a pair of spin 1 particle in singlet state. So can determine the value for Si without disturbing that system, leading the non-contextuality. R.A. Bertlmann & A. Zeilinger quantum [un]speakables from Bell to quantum information

  16. L. Hardy: two spin one half particles. Jordan proved that for the state like: If there exist four projection operators satisfy: PRA50, 62(1994) Jordan But because of 2 & 3. If D=1 then G=1. If E=1 then F=1. So if the probability that D=E=1 is not 0, then the probability for F=G=1 won’t be 0.

  17. Consider the CH inequality: PRD10, 526 (1974) 3 4 1 2 Eberhard Inequality Compare to previous page: PRA52, 2535 (1995) Garuccio

  18. A. Bramon, and G. Garbarino: PRL88, 040403 (2002), PRL89, 160401 (2002). Quant-ph/05011069. A. Bramon, R. Escribano and G. Garbarino: Hardy type experiment with entangled Kaon pairs • Generate a asymmetric state. • Eberhard’s inequality (EI).

  19. To generate the asymmetric state, fix a thin regenerator on the right beam close to decay points. Then the initial state: Becomes: Let this state propagate to a proper time T:

  20. where component has been enhanced. has been further suppressed. Normalize it to the surviving pairs leads to:

  21. 4.The Feasibility of Testing LHVTs in Charm factory • Easy to get space-like separation. • Can test the phenomena: less entangled state leads to larger violation of inequality. In the charm factory the entanglement state formed as: where

  22. The four joint measurement of the transition probability needed in the EI predicted by QM take the following form:

  23. (for See figure 3) Take into EI: where is the violation degree of the inequality. From QM we have: First assume See Figure 1

  24. Actually has non-zero magnitude : 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.

  25. The advantage of over To make sure the misidentification of is of order per thousand Properly choose PRL88, 040403 (2002) Space-like separation required: In factory so Charm factory so has a wider region of R in discriminating QM from LHVT. There is phenomena can be test due to this advantage.

  26. Quantify the entanglement 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. To see this we must quantify the degree of entanglement Take concurrence as a measure of this quantity. Where: W. Wootters PRL80, 2245 (1998) C changes between 0 to 1 for no entanglement and full entanglement. This mean the state become less entangled during time evolution!

  27. Expressthe violation in degree ofentanglement 1.The usual CHSH inequality: N.Gisin PLA154,201(1991) Abouraddy et al. PRA64,050101,(2001) 2. The Hardy state using Eberhard’s inequality : See the figure next page Note we make a trick in the figure that substitute C with

  28. The Entanglement and Bell inequality violation Magnitudesbelow zero of VD is the range of violation

  29. Thank you for your patience.

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