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Animations of three famous quantum experiments are presented. PowerPoint Presentation

Animations of three famous quantum experiments are presented.

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Animations of three famous quantum experiments are presented.

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Animations of three famous quantum experiments are presented.

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- Animations of three famous quantum experiments are presented.
- The violation of Bell inequalities with entangled photons,
- 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

A+

Eigendirections

of apparatus A

A-

Calcite

A

A+

(A-,α)=cos αP(A-)=cos2α

α

A-

(A+,α)=cos(90-α)=sin α P(A+)=sin2α

B+

Different

eigendirections

belong to B

Calcite

B-

B

Source of

photon

pairs

Calcite

Calcite

A+

A-

A

A

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:

B+

either

Source of

photon

pairs

Calcite

Calcite

A-

B-

or

B

A

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 measuredpairs.

E.gN(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+)

Bell P(A+,C+) <P(B+,C+) + P(A+,B+)

Quant.Mech:P(A+,C+) =

P(B+,C+ )=

P(A+,B+) =

Q.M. violates

Bell inequalities!

Innsbruck experiment

The unknown state to be teleported is carried by photon (1):

| 1 = ( | ↔ 1 + | ↕ 1 ),

with certain coefficients and :| |2 + | |2 = 1EPR-pair of photons: numbered 2 and 3 are created from a BBO crystal

Teleportation formalism

| 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.

Bell inequalities

Quantum Cryptography

Teleportation