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quantum teleportation PowerPoint PPT Presentation


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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

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quantum teleportation

David Riethmiller

28 May 2007


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The EPR Paradox

  • Einstein, Podolsky, Rosen – 1935 paper

  • Concluded quantum mechanics is not “complete.”


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Spacelike Separation

The EPR Paradox

Spin zero

Copenhagen Interpretation of QM:

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


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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.”


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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”


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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.


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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.


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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.


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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.


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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.


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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.


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Teleportation

  • Two spin-1/2 particles are prepared in an EPR singlet state:

  • The pair is separated and distributed to Alice and Bob.


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Teleportation

  • Writing the state of the initial particle as:

  • Note that initially Alice has a pure product state:


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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.


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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.


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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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