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## PowerPoint Slideshow about 'Quantum teleportation' - Faraday

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The EPR Paradox

- Einstein, Podolsky, Rosen – 1935 paper
- Concluded quantum mechanics is not “complete.”

The EPR Paradox

Spin zero

Copenhagen Interpretation of QM:

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

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

- 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 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 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

- 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 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

- 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.

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

- Two spin-1/2 particles are prepared in an EPR singlet state:
- The pair is separated and distributed to Alice and Bob.

Teleportation

- Writing the state of the initial particle as:
- Note that initially Alice has a pure product state:

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.

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

- 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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