Entanglement. Michelle Victora Advisor: Paul G. Kwiat. Physics 403 talk: March 13, 2017

Transcription

1 Entanglement Michelle Victora Advisor: Paul G. Kwiat Physics 403 talk: March 13, 2017

2 Introduction to entanglement Making entanglement in the lab Applications

3 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 )

4 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 )

5 Is this state entangled? No! ȁψ AB = 1 2 ( ȁh A + ȁv )(ȁ A H B + ȁv B )

6 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?

7 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!

8 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?

9 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!

10 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 = Didn t rise early = 39.2

11 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

12 Potential Loopholes

13 Potential Loopholes Detection Efficiency/Fair Sampling Assumption

14 Potential Loopholes Detection Efficiency/Fair Sampling Assumption Communication/Locality Loophole

15 Basic introduction to entanglement Making entanglement in the lab Applications

16 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

17 Downconversion is polarization-dependent Vertical Horizontal Horizontal Horizontal Vertical Vertical

18 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

19 Basic introduction to entanglement Making entanglement in the lab Applications

20 Quantum Teleportation

21 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

22 Quantum Teleportation Total System of Three Particles

23 Quantum Teleportation Total System of Three Particles Which equals

24 Quantum Teleportation

25 But wait, there s more!

26 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 = 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

27 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 = 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

28 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

29 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