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Quantum Entanglement and Applications
Trent Graham
Advisor: Paul Kwiat December 3, 2013
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Contents
What is Entanglement Entanglement Creation
Applications
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Contents
What is Entanglement Entanglement Creation
Applications
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Entanglement is a feature of compound quantum systems
States that can be written are separable
States that cannot be written this way are entangled
Measurement outcomes are random and correlated
No solution!
Example: the Bell states & are inseparable
Ψ AB = φ1 A φ2 B
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What's so special about entanglement?
Classical things can be random and correlated, too…
Entangled systems give random and correlated measurement outcomes
in every measurement basis!
… but not entangled!
Each marble has a defined color from the beginning (local hidden variable)
The processes are distinguishable in principle
There is no conjugate measurement basis
How is this different from an entangled state?
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Contents
What is Entanglement Entanglement Creation
Applications
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Spontaneous Parametric Down Conversion
1 2p
1 2pp p p
pp
1p2p
• Nonlinear crystals (such as BBO) have a small chance of splitting a high-energy photon into two low-energy photons*.
• Daughter photons diverge in a cone from the source because of energy and momentum conservation.
* Burnham and Weinberg, PRL 25, 84 (1970)
VH
H
H
V
V
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Polarization Entanglement
• A polarization entangled state can be created by pumping two orthogonally oriented crystals with a superposition of H and V polarization*.
• The two-photon state can be controlled by manipulating the pump polarization state.
* Kwiat et al., PRA 60, R773 (1999)
1
2V H 1 2 1 2
1
2H H V V
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Temporal-Mode Entanglement*
• A temporal-mode entangled state can be created by pumping a nonlinear crystal with a coherent superposition of pulses.
s f
1
2s f 1 2 1 2
1
2s s f f
* Brendel et al., PRL 82, 2594 (1999)
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Orbital Angular Momentum Entanglement*
g
1 2 1 2 1 2...N g g
• Conservation of orbital angular momentum photons are always correlated in spatial mode.
• A combination of fibers and holograms are used to filter out all but the ±1 orbital angular momentum modes.
g
* Barreiro et al., PRL 95, 260501 (2005)
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Hyperentanglement
• By combining these techniques, we create states simultaneously entangled in multiple degrees of freedom*.
1
2HH VV
* Barreiro et al., PRL 95, 260501 (2005)
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Contents
What is Entanglement Entanglement Creation
Applications
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Super-Dense Coding
• Super-dense coding may be used to communicate a 2-bit message with a single transmitted qubit*.
• Bob can only distinguish three Bell states limiting this technique to 1.59 bits/photon**.
* Bennett and Wiesner, PRL 69, 2881 (1992)
** Mattle et al., PRL 76, 4656–4659 (1996)
1
2HH VV
1
2HH VV
1
2HV VH
1
2HV VH
1
2HH VV
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Quantum Teleportation
• Quantum teleportation can be used to teleport a qubit with a
2-bit message over classical communication channel*.
• The utility of this technique is limited because of the required Bell state measurement**.
* Bennett and Wiesner, PRL 69, 2881 (1992)
** Vaidman and Yoran, PRA 59, 116 (1999)
1[ 0 1 0 1
2
1 0 1 0 ]
0 1
0 1
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Summary
Entanglement is a type of correlation between quantum
systems that is stronger than any classical correlation
Entangled systems cannot be completely described independently
Entanglement plays a central role in quantum information applications
Entanglement is fairly easy to create in the lab