Borss, K' Benedict, M' G' University of Szeged, Szeged, Hungary Animation of experiments in modern q

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Borsós, K. Benedict, M. G. University of
Szeged, Szeged, HungaryAnimation of experiments
in modern quantum physics

• Animations of three famous quantum experiments
  are presented.
• The violation of Bell inequalities with entangled
  photons,
• Quantum-teleportation of a photon polarization
  state,
• 3) Secret key (BB84) generation for
  quantum-cryptography. The animations are to be
  used as demonstrations complementing
• lectures in modern Quantum Mechanics and/or
  Quantum Informatics.
• The following 9 slides sketch the background.
• Clicking on the title, or on the text of the
  last slide starts the animation

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Polarization of photons
A
Eigendirections of apparatus A
A-
Calcite
A
A
(A-,a)cos a P(A-)cos2 a
a
A-
(A, a)cos(90- a)sin a P(A)sin2 a
3
B
Different eigendirections belong to B
Calcite
B-
B
4
EPR experiment with photon pairs
Source of photon pairs
Calcite
Calcite
A
A-
A
A
Strict correlation between the two outputs. We
need not even measure on the left if we know the
result on the right. But we can measure
incompatible quantities (observaables) on the two
sides
B
either
Source of photon pairs
Calcite
Calcite
A-
B-
or
B
A
5
Presentation of a Bell inequality
N(A,C-) lt N(B,C-) N(A,B-)
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We cannot measure two different properties on
the same particle, because measurment changes the
state. Therefore we measure on pairs flying in
different directions. The orientation of the
crystal A, B or C is chosen randomly.

• N(A,C-) lt N(B,C-) N(A,B-)
  Bell
• N(A,C) lt N(B,C) N(A,B)
• Bold N is the number of measured pairs.
• E.g N(A,C) the number of pairs with outcome A
  on the left, and C on the right.
• This can be measured!

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Bell N(A,C) lt N(B,C)
N(A,B)
Bell P(A,C) lt P(B,C)
P(A,B)
Quant.Mech P(A,C)
P(B,C )
P(A,B)
Q.M. violates Bell inequalities!
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BB84 cryptography
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Teleportation experiment
Innsbruck experiment
The unknown state to be teleported is carried by
photon (1) ? ?1 ( ? ? ?1 ? ? ?1 ),
with certain coefficients ? and ? ? 2
? 2 1EPR-pair of photons numbered 2 and
3 are created from a BBO crystal
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Teleportation formalism
?tot ? ? ?1 ? ?- ?23 ( ? ? ?1
? ? ?1 ) ? (1/v2)( ? ?2 ? ?3 - ? ?2 ?
?3 ) ?tot ? (1/v2) ( ? ? ?3 - ? ? ?3 )
? ?12 - ( ? ? ?3 ? ? ?3 ) ?- ?12
( ? ? ?3 ? ? ?3 ) ? ?12 ( ? ? ?3 -
? ? ?3 ) ?- ?12
Photon (1) goes through a polarizer which
establishes a polarization direction, then goes
to Alice. Photon (3) arrives to Alice. Its
entangled pair (3) goes to Bob The joint state
of (1) and (2) is measured by D1 and D2 at
Alice The two detectors have 4 different output
results 0,1,2,3. The result is communicated to
Bob through a classical channel. Bob performs an
appropriate (unitary) transformation on photon
(3) depending on the message he received. The
resulting state of (3) will be identical to the
state of (1it was.
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Animation

• Bell inequalities
• Quantum Cryptography
• Teleportation