Entanglement Michelle Victora Advisor: Paul G. Kwiat Physics 403 talk: March 13, 2017
Introduction to entanglement Making entanglement in the lab Applications
Quantum states describing more than one system can be separable or entangled System A (a photon) System B (another photon) ȁ Ψ AB = Two-photon state of A and B States that can be written ȁψ AB = ȁφ 1 A ȁ are separable Example: ȁ Ψ AB = ȁh A ȁ V B φ2 B States that cannot be written this way are entangled Example: ȁ Ψ AB = 1 (ȁh 2 A ȁv B + ȁv A ȁh B )
Is this state entangled? ȁψ AB = 1 2 ( ȁh ȁ A V B + ȁv ȁ A H +ȁ B V ȁ A V B + ȁh ȁ A H B )
Is this state entangled? No! ȁψ AB = 1 2 ( ȁh A + ȁv )(ȁ A H B + ȁv B )
Measurement outcomes are random and correlated ȁψ AB = 1 2 ( ȁh ȁ A V B + ȁv ȁ A H B ) 50% chance to measure H or V for either photon (random) But the photons always have orthogonal polarization (correlated) But classical things can be random and correlated too what s special about entanglement?
Quantum cakes Lucy Ricardo Does the cake taste good or bad? Has the cake risen or not risen early? Only one measurement can be made on any particular cake!
Lucy and Ricardo randomly decide which measurement to make on each cake, and record their results. There are three cases: 1. They both check their ovens midway 9% of the time, both cakes rise early (the rest of the time, only one or neither does) 2. One checks midway and the other waits Whenever Lucy s cake rises early, Ricardo s tastes good Whenever Ricardo s cake rises early, Lucy s tastes good 3. They both wait Do the cakes taste good or bad?
When they both check midway 9% of the time, both cakes rise early Whenever Lucy s cake rises early, Ricardo s cake tastes good Whenever Ricardo s cake rises early, Lucy s cake tastes good When they both wait How often do both cakes taste good? Both cakes never taste good!
This experiment isn t really possible with cakes, but it is possible with photons Tasted good Source θ Rose early Tasted bad Didn t rise early Tasted good = 0 (horizontal) Tasted bad = 90 (vertical) Rose early = -50.8 Didn t rise early = 39.2
This all means that entanglement violates local realism Realism = all physical properties (tasting good or bad) are defined, even if we don t measure them Local = measurements of one thing don t affect another (possibly far away) thing
Potential Loopholes
Potential Loopholes Detection Efficiency/Fair Sampling Assumption
Potential Loopholes Detection Efficiency/Fair Sampling Assumption Communication/Locality Loophole
Basic introduction to entanglement Making entanglement in the lab Applications
Downconversion produces pairs of photons Laser Momentum conservation k 1 k 2 ω laser ω 1 ω 2 Energy conservation Nonlinear crystal k laser Source: David Guzman, Universidad de los Andes
Downconversion is polarization-dependent Vertical Horizontal Horizontal Horizontal Vertical Vertical
Two crystals can create polarization entanglement Horizontal Vertical ȁv หH ȁh ȁh หV ȁv Superposition Polarization entanglement ȁh + e iφ ȁv หV ȁv + e iφ หH ȁh
Basic introduction to entanglement Making entanglement in the lab Applications
Quantum Teleportation
Lucy wants to communicate an unknown quantum state to Ricardo Bell-state measurement Ricardo now has the state of photon 1 Unitary Transformation Lucy Unknown state: photon 1 2 3
Quantum Teleportation Total System of Three Particles
Quantum Teleportation Total System of Three Particles Which equals
Quantum Teleportation
But wait, there s more!
Classical Cryptography One-Time Pad Alice uses a one-time pad that she shares with Bob to encode a message. Bob uses his identical one-time pad to decode Alice s string Y 0 1 1 1 1 0 0 1 + 1 0 0 0 1 1 1 0 = 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1-1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 Y Not random + Completely random = Completely random Message + Secret key - Secret Key = Message Without access to the completely random key, it is impossible for Eve to decode the string
Classical Cryptography Quantum One-Time Pad Quantum Key Distribution Alice uses a one-time pad that she shares with Bob to encode a message. Bob uses his identical one-time pad to decode Alice s string Y 0 1 1 1 1 0 0 1 + 1 0 0 0 1 1 1 0 = 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1-1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 Y Not random + Completely random = Completely random Message + Secret key - Secret Key = Message Without access to the completely random key, it is impossible for Eve to decode the string
C. H. Bennett and G. Brassard, Quantum Cryptography: Public key distribution and coin tossing, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, 175 (1984). Quantum Key Distribution Detectors Entanglement Source HWP + PBS Alice Eve Bob Alice's Basis Choice: H/V H/V H/V H/V D/A D/A H/V D/A Alice's Measurements: H V H H A D V A Eve Basis Choice: D/A D/A D/A H/V D/A D/A D/A H/V Eve's Measurements: D A D H A D D V Bob's Basis Choice: D/A H/V H/V H/V D/A H/V H/V D/A Bob's Measurements: D V V H A V H A
Summary Entangled systems can t be completely described independently (not separable) Entanglement is a type of correlation between quantum systems that is stronger than any classical correlation, and violates local realism Entanglement is fairly easy to create in the lab Entanglement plays a central role in quantum information applications