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Entanglement and Bell’s Inequalities

Entanglement and Bell’s Inequalities. Aaron Michalko Kyle Coapman Alberto Sepulveda James MacNeil Madhu Ashok Brian Sheffler. Correlation. Drawer of Socks 2 colors, Red and Blue, Four combinations: RR, RB, BR, BB (pR 1 + qB 1 ) (pR 2 + qB 2 ) 50% Same, 50% Different NO CORRELATION.

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Entanglement and Bell’s Inequalities

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  1. Entanglement and Bell’s Inequalities Aaron Michalko Kyle Coapman Alberto Sepulveda James MacNeil Madhu Ashok Brian Sheffler

  2. Correlation • Drawer of Socks • 2 colors, Red and Blue, • Four combinations: RR, RB, BR, BB • (pR1 + qB1) (pR2 + qB2) • 50% Same, 50% Different • NO CORRELATION

  3. Correlation • What if socks are paired: RR, BB • If you know one, you know the other • 100% Same, 0% Different • Perfectly Correlated • Entanglement ~ Correlation

  4. What is Entanglement? • Correlation in all bases • What is a basis? • Like a set of axes • Our basis is polarization: V and H • Photons either VV or HH • Perfectly correlated

  5. How do we Entangle Photons? • Parametric down conversion • Non-linear, birefringent crystal • 2 emitted photons, signal and idler

  6. How do we Entangle Photons? • 2 crystals create overlapping cones of photons • Photons are entangled: • We don’t know if any photon is VV or HH…or maybe both…

  7. Logic Exercise • Three Assumptions: • When a photon leaves the source it is either H or V • No communication between photons after emission • Nothing that we don’t know, V/H is a complete description

  8. Logic Exercise • Polarizers set at 45 • 50% transmit at each polarizer • Logical Conclusion: • 25% Coincident • 50% One at a time • 25% No Detection >>> NO CORRELATION

  9. Logic Exercise • Entangled Source • 50% coincidence reading • 50% no reading • >>>100% Correlation

  10. Lab setup

  11. Lab setup

  12. Lab Activity 1 • We measured the coincidence counts of entangled photons • Each passed through a polarizer set at the same angle

  13. Lab Activity 2 • We only changed one polarizer angle this time • What do you think will happen?

  14. Logic Exercise • Which assumption is incorrect: • Reality • Locality • Hidden Variables

  15. Bell’s Inequalities • Let A,B and C be three binary characteristics. • Assumptions: Logic is valid. The parameters exist whether they are measured or not. • No statistical assumptions necessary! • Let’s try it!

  16. CHSH Bell’s Inequality • Let’s define a measure of correlation E: • If E=1, perfect correlation. • If E=-1, perfect anticorrelation.

  17. Hidden Variable Theory • Deterministic • Assumes Polarization always has a definite value that is controlled by a variable • We’ll call the variable λ

  18. HVT v. QM • Comparing PVV for HVT and QM looks like: • The look pretty close…but HVT is linear

  19. CHSH Bell’s Inequality cont. • Let’s introduce a second measure of correlation: • According to HVT S≤2 for any angle.

  20. CHSH Bell’s Inequality cont. • QM predicts S≥2 in some cases. • a=-45°, a’=0°, b=22.5°, b’=-22.5° • S(QM)=2.828 S(HVT)=2 • This means that either locality or reality are false assumptions!

  21. Our Lab Activity • We recorded coincidence counts with combinations of | polarization angles • S = 2.25 • We violated Bell’s inequality! That means our system is inherently quantum, and cannot be explained using classical physics

  22. This is a little scary… • HVT is not a valid explanation for the behavior of entangled photons • So…that means we either violate: • Reality • Locality

  23. Thank You George!!!

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