Borsós, K.; Benedict, M. G. University of Szeged, Szeged, Hungary Animation of experiments in modern quantum physics Animation of experiments in modern quantum physics Animations of three famous quantum experiments are presented. 1)The violation of Bell inequalities with entangled photons, 2) Quantum-teleportation of a photon polarization state, 3) Secret key (BB84) generation for quantum-cryptography. The animations are to be used as demonstrations complementing lectures in modern Quantum Mechanics and/or Quantum Informatics. The following 9 slides sketch the background. Clicking on the title, or on the text of the last slide starts the animation

Polarization of photons Calcite α A- A+ (A-, α )=cos α P(A-)=cos 2 α A+ A- Eigendirections of apparatus A A (A+, α )=cos(90- α )=sin α P(A+)=sin 2 α

Calcite B+ B- Different eigendirections belong to B B

EPR experiment with photon pairs Source of photon pairs Calcite Strict correlation between the two outputs. We need not even measure on the left if we know the result on the right. But we can measure incompatible quantities (observaables) on the two sides: Source of photon pairs Calcite B- A+ A- AA A B B+ either or

Presentation of a Bell inequality N(A+,C-) < N(B+,C-) + N(A+,B-)

We cannot measure two different properties on the same particle, because measurment changes the state. Therefore we measure on pairs flying in different directions. The orientation of the crystal A, B or C is chosen randomly. N(A+,C-) < N(B+,C-) + N(A+,B-) Bell N (A+,C+) < N (B+,C+) + N (A+,B+) Bold N is the number of measured pairs. E.g N (A+,C+) the number of pairs with outcome A+ on the left, and C+ on the right. This can be measured! :

Bell: N(A+,C+) < N(B+,C+) + N(A+,B+) Quant.Mech : P(A+,C+) = Bell P(A+,C+) < P(B+,C+) + P(A+,B+) P(B+,C+ )= P(A+,B+) = Q.M. violates Bell inequalities!

BB84 cryptography

Teleportation experiment Innsbruck experiment The unknown state to be teleported is carried by photon (1): |   1 = (  | ↔  1 +  | ↕  1 ), with certain coefficients  and  : |  | 2 + |  | 2 = 1 EPR-pair of photons: numbered 2 and 3 are created from a BBO crystal

|  tot  = |   1  |  -  23 = (  | ↔  1 +  | ↕  1 )  (1/√2)( | ↔  2 | ↕  3 - | ↕  2 | ↔  3 )= |  tot  = (1/√2)[ (  | ↔  3 -  | ↕  3 ) |  +  12 - (  | ↔  3 +  | ↕  3 ) |  -  12 – + (  | ↕  3 +  | ↔  3 ) |  +  12 + (  | ↕  3 -  | ↔  3 ) |  -  12 Photon (1) goes through a polarizer which establishes a polarization direction, then goes to Alice. Photon (3) arrives to Alice. Its entangled pair (3) goes to Bob The joint state of (1) and (2) is measured by D1 and D2 at Alice The two detectors have 4 different output results 0,1,2,3. The result is communicated to Bob through a classical channel. Bob performs an appropriate (unitary) transformation on photon (3) depending on the message he received. The resulting state of (3) will be identical to the state of (1it was. Teleportation formalism

Animation Bell inequalities Quantum Cryptography Teleportation