quantum teleportation

1. quantum teleportation David Riethmiller 28 May 2007

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

3. Spacelike Separation The EPR Paradox Spin zero Copenhagen Interpretation of QM: no state is attributable to a particle until that state is measured.

4. 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.”

5. 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”

6. 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.

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.

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

13. Teleportation • Writing the state of the initial particle as: • Note that initially Alice has a pure product state:

14. 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.

15. 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.

16. 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