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 • (pR1 + qB1) (pR2 + qB2) • 50% Same, 50% Different • NO CORRELATION

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

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

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

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…

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

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

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

Lab setup

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

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

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

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!

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

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

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

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

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!

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

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

Thank You George!!!

Entanglement and Bell’s Inequalities