# 1 quantum teleportation David Riethmiller 28 May 2007.

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1 quantum teleportation David Riethmiller 28 May 2007

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

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

4 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.” Spacelike Separation

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 Alice has 2 classical options: –1–1) She can try to physically transport this info to Bob. –2–2) 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. –N–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. –Q–Quantum measurement is unreliable unless Alice knows beforehand that her state belongs to an orthonormal set.

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

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