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quantum teleportation. David Riethmiller 28 May 2007. The EPR Paradox. Einstein, Podolsky, Rosen – 1935 paper Concluded quantum mechanics is not “complete.”. Spacelike Separation. The EPR Paradox. Spin zero. Copenhagen Interpretation of QM:

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quantum teleportation

David Riethmiller

28 May 2007

the epr paradox
The EPR Paradox
  • Einstein, Podolsky, Rosen – 1935 paper
  • Concluded quantum mechanics is not “complete.”
the epr paradox3

Spacelike Separation

The EPR Paradox

Spin zero

Copenhagen Interpretation of QM:

no state is attributable to a particle until that state is measured.

the epr paradox4

Spacelike Separation

The EPR Paradox
  • Measurement on one particle collapses wave functions of both
  • Appear to have superluminal propagation of information
  • If we can’t account for “hidden variables” which allow this propagation, QM must not be “complete.”
non locality and bell s inequalities
Non-Locality and Bell’s Inequalities
  • Local Interactions
    • Particle interacts only with adjacent particles
  • Non-Local Interactions
    • Particle allowed to interact with non-adjacent particles
    • “Action at a distance”
non locality and bell s inequalities6
Non-Locality and Bell’s Inequalities
  • J.S. Bell, 1964
    • Calculated series of inequalities based on probability of measuring entangled (correlated) photons in certain states
    • If observations obeyed these inequalities, only LOCAL interactions allowed
    • If observations violated inequalities, NON-LOCAL interactions allowed.
non locality and bell s inequalities7
Non-Locality and Bell’s Inequalities
  • Experiments showed violation of Bell’s Inequalites.
  • Then non-locality is a necessary condition to arrive at the statistical predictions of quantum mechanics.
  • Gives rise to principle mechanism behind quantum teleportation.
meet alice and bob
Meet Alice and Bob
  • Let’s say Alice has some arbitrary quantum particle in state |f> that she doesn’t know, but she wants to send this information to Bob.
meet alice and bob9
Meet Alice and Bob
  • Alice has 2 classical options:
    • 1) She can try to physically transport this info to Bob.
    • 2) She can measure the state in her possession and communicate the measurement to Bob, who prepares an identical state.
problems
Problems
  • 1) She can try to physically transport this info to Bob.
    • Not a good idea. Quantum states are fragile and unstable under small perturbations. It will never reach Bob without being perturbed out of its original state.
problems11
Problems
  • 2) She can measure the state in her possession and communicate the measurement to Bob, who prepares an identical state.
    • Quantum measurement is unreliable unless Alice knows beforehand that her state belongs to an orthonormal set.
teleportation
Teleportation
  • Two spin-1/2 particles are prepared in an EPR singlet state:
  • The pair is separated and distributed to Alice and Bob.
teleportation13
Teleportation
  • Writing the state of the initial particle as:
  • Note that initially Alice has a pure product state:
teleportation14
Teleportation
  • Alice’s measurement on her own correlated system collapses the wave functions of BOTH EPR particles, since they are entangled.
  • All Alice has to do is communicate the (classical) results of her measurement to Bob.
teleportation15
Teleportation
  • Bob’s EPR particle wave function has been collapsed – Alice just needs to tell him HOW it should collapse, according to her measurement:
  • Bob only needs to know which of the unitary transformations to apply in order to reconstruct |f>, and the teleportation is complete.
conclusions
Conclusions
  • Non-locality necessary condition to for statistical predictions of QM
  • QM Complete?
    • Complete enough to predict states of EPR pairs
  • Predictions principle mechanism behind quantum teleportation
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