The Feasibility of Testing LHVTs in High Energy Physics

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The Feasibility of Testing LHVTs in High
Energy Physics
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Phys.Rev. D74,076003, (2006)
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In corporation with ??? ??
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Content

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

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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
  operators can not have simultaneously reality. or
  II. QM is incomplete.

Einstein, Podolsky, Rosen. 1935
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EPR ( Bohms version)
Two different measurements may performe upon the
first particle. Due to angular momentum
conservation and Einsteins argument of reality
and locality, the quantities of Non-commuting
operators of the second particle can be
simultaneously reality.
So QM is incomplete !
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Bohrs 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
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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) Dgt3 paradox.
Bell
D2. Bell inequality(1964). Dgt3. contextual
dependent hidden variable theorem would survive.

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

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Mass eigenstates
CP eigenstates
S eigenstates
1
Like the photon case they dont 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.
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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)
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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
Hardys proof relies on a certain lack of
symmetry of the entangled state.
PRL71, 1665 (1993)
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GHZ states three spin half particles.
which contradict (4).
No reasonable definition of reality could be
expected to permit this.
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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
unspeakables from Bell to quantum information
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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 D1 then G1. If E1
then F1.
So if the probability that DE1 is not 0, then
the probability for FG1 wont be 0.
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Eberhard Inequality
Compare to previous page
PRA52, 2535 (1995) Garuccio
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Hardy type experiment with entangled Kaon pairs

• Generate a asymmetric state.
• Eberhards inequality (EI).

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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
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component has been enhanced.
has been further suppressed.
Normalize it to the surviving pairs leads to
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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
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The four joint measurement of the transition
probability needed in the EI predicted by QM take
the following form
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Take into EI
where
is the violation degree of the inequality.
From QM we have
First assume
See Figure 1
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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.
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The advantage of over
To make sure the misidentification of
is of order per thousand
Properly choose
PRL88, 040403 (2002)
Space-like separation required
factory
In
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.
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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
PRL80, 2245 (1998)
W. Wootters
C changes between 0 to 1 for no entanglement and
full entanglement.
This mean the state become less entangled during
time evolution!
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Express the violation in degree of entanglement
1.The usual CHSH inequality
PLA154,201(1991)
N.Gisin
Abouraddy et al.
PRA64,050101,(2001)
2. The Hardy state using Eberhards inequality
See the figure next page
Note we make a trick in the figure that
substitute C with
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The Entanglement and Bell inequality violation
Magnitudes below zero of VD is the range of
violation
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Thank you for your patience.