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 [( ω 0 − ω ) t/ 2] � 2 ( ω 0 − ω ) 2 0.25 0.2 0.15 0.1 0.05 2 4 6 8 10 12 14

P a → b ( ω ) P a → b ( t ) ≈ | V ab | 2 sin 2 [( ω 0 − ω ) t/ 2] � 2 ( ω 0 − ω ) 2

P a → b ( ω ) P a → b ( t ) ≈ | V ab | 2 sin 2 [( ω 0 − ω ) t/ 2] � 2 ( ω 0 − ω ) 2

Quantum Teleportation

Time Evolution e − i E t/ � ψ ( x ) energy eigenstate: e − i H ∆ t/ � ψ ( x ) small � t: e − i H ∆ t 2 / � e − i H ∆ t 1 / � ψ ( x ) R t 0 H dt/ � ψ ( x ) in general: T e − i Unitary Matrix U † U = 1

Entangled States two electrons in spin zero state 1 √ 2 ( | ↑↓� − | ↓↑� ) take one electron light years away as soon one spin is measured the other is determined Einstein hated this “spooky action at a distance”

Entangled States two electrons in spin zero state 1 √ 2 ( | ↑↓� − | ↓↑� ) take one electron light years away as soon one spin is measured the other is determined Einstein hated this “spooky action at a distance”

Preparing to Teleport Alice has an electron is some quantum state | ψ 1 � = α | ↑� + β | ↓� she prepares electrons 2 and 3 in a spin zero state | ψ ( − ) 1 23 � = 2 ( | ↑↓� − | ↓↑� ) √ she give electron 3 to Bob who goes to the teleport destination | ψ 1 � ⊗ | ψ ( − ) | Γ 123 � = 23 � β α = 2 ( | ↑↑↓� − | ↑↓↑� ) + 2 ( | ↓↑↓� − | ↓↓↑� ) √ √

Quantum Teleportation Alice performs a measurement with 4 possible outcomes | ψ ( ± ) 1 12 � = 2 ( | ↑↓� ±| ↓↑� ) √ | φ ( ± ) 1 12 � = 2 ( | ↑↑� ±| ↓↓� ) √ 1 = | ψ ( − ) 12 �� ψ ( − ) 12 | + | ψ (+) 12 �� ψ (+) 12 | + | φ ( − ) 12 �� φ ( − ) 12 | + | φ (+) 12 �� φ (+) 12 | | �� | | �� | | �� | | �� | � � new state: � | ψ − 12 � ( − α | ↑�− β | ↓� ) + | ψ + � 12 � ( − α | ↑� + β | ↓� ) 1 | Γ 123 � = 12 � ( α | ↓� + β | ↑� ) + | φ + 2 + | φ − 12 � ( α | ↓�− β | ↑� )

Quantum Teleportation 4 possible states each with probability 1/ 4 | ψ ( − ) if Alice finds for example, she tells Bob: 12 � | ψ 3 � = − α | ↑�− β | ↓� Bob does unitary transformation: � � � � � � − 1 − α α 0 = − 1 − β β 0 Bob’ s electron is now in first electron’ s initial state: � � � � � | ψ 3 � = α | ↑� + β | ↓�

Quantum Teleportation � � � � � � − − similarly � � � � � � − 1 − α α 0 | ψ (+) 12 � : = β β 0 1 � � � � � � β α 0 1 | φ ( − ) 12 � : = α β 1 0 � � � � � � − β α 0 1 | φ (+) 12 � : = − 1 α β 0 | ψ 3 � = α | ↑� + β | ↓�

Quantum Teleportation electron 3 is in original state electron 1 is in some new state no one ever found out what and are β α