SLIDE 1
2 4 6 8 10 12 14 0.05 0.1 0.15 0.2 0.25
Pa→b(t)
Pa→b(t) ≈ |Vab|2
2 sin2[(ω0−ω)t/2] (ω0−ω)2
Pa→b(ω)
Pa→b(t) ≈ |Vab|2
2 sin2[(ω0−ω)t/2] (ω0−ω)2
P a b ( t ) P a b ( t ) | V ab | 2 sin 2 [( 0 ) t/ 2] 2 ( 0 - - PowerPoint PPT Presentation
P a b ( t ) P a b ( t ) | V ab | 2 sin 2 [( 0 ) t/ 2] 2 ( 0 - - PowerPoint PPT Presentation
P a b ( t ) P a b ( t ) | V ab | 2 sin 2 [( 0 ) t/ 2] 2 ( 0 ) 2 0.25 0.2 0.15 0.1 0.05 2 4 6 8 10 12 14 P a b ( ) P a b ( t ) | V ab | 2 sin 2 [( 0 ) t/ 2] 2 ( 0
SLIDE 2
SLIDE 3
Pa→b(ω)
Pa→b(t) ≈ |Vab|2
2 sin2[(ω0−ω)t/2] (ω0−ω)2
SLIDE 4
Quantum Teleportation
SLIDE 5
Time Evolution
energy eigenstate: e−i E t/ ψ(x) in general: e−i H ∆t/ ψ(x) e−i H ∆t2/ e−i H ∆t1/ ψ(x) T e−i
R t
0 H dt/ ψ(x)
small t: Unitary Matrix U †U = 1
SLIDE 6
Entangled States
two electrons in spin zero state 1 √ 2 (| ↑↓ − | ↓↑) take one electron light years away as soon one spin is measured the
- ther is determined
Einstein hated this “spooky action at a distance”
SLIDE 7
Entangled States
two electrons in spin zero state 1 √ 2 (| ↑↓ − | ↓↑) take one electron light years away as soon one spin is measured the
- ther is determined
Einstein hated this “spooky action at a distance”
SLIDE 8
|ψ(−)
23 = 1 √ 2 (|↑↓ − |↓↑)
|ψ1 = α|↑ + β|↓
Preparing to Teleport
she prepares electrons 2 and 3 in a spin zero state she give electron 3 to Bob who goes to the teleport destination Alice has an electron is some quantum state
|Γ123 = |ψ1 ⊗ |ψ(−)
23
=
α √ 2 (|↑↑↓ − |↑↓↑) + β √ 2 (|↓↑↓ − |↓↓↑)
SLIDE 9
|
- |
|
- |
|
- |
|
- |
|Γ123 =
1 2
|ψ−
12 (−α |↑−β |↓) + |ψ+ 12 (−α |↑+β |↓)
+ |φ−
12 (α |↓+β |↑) + |φ+ 12 (α |↓−β |↑)
- Quantum Teleportation
Alice performs a measurement with 4 possible outcomes
|ψ(±)
12 = 1 √ 2 (|↑↓ ±| ↓↑)
|φ(±)
12 = 1 √ 2 (|↑↑ ±| ↓↓)
1 = |ψ(−)
12 ψ(−) 12 | + |ψ(+) 12 ψ(+) 12 | + |φ(−) 12 φ(−) 12 | + |φ(+) 12 φ(+) 12 |
- new state:
SLIDE 10
|ψ(−)
12
4 possible states each with probability 1/ 4 if Alice finds for example, she tells Bob:
Quantum Teleportation
|ψ3 = −α |↑−β |↓
- −1
−1 −α −β
- =
- α
β
- Bob does unitary transformation:
|ψ3 = α |↑ + β |↓
Bob’ s electron is now in first electron’ s initial state:
SLIDE 11
similarly
Quantum Teleportation
|ψ3 = α |↑ + β |↓
- −
−
- |ψ(+)
12 :
- −1
1 −α β
- =
- α
β
- |φ(−)
12 :
- 1
1 β α
- =
- α
β
- |φ(+)
12 :
- 1
−1 −β α
- =
- α
β
SLIDE 12
Quantum Teleportation
electron 3 is in original state electron 1 is in some new state no one ever found out what and are α β