Introduction: Quantum Correlations
Entanglement is a uniquely quantum phenomenon where particles become correlated in ways that can't be explained by classical physics. Einstein called it "spooky action at a distance."
The Entangled State
Consider the singlet state of two spins:
\[|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|\uparrow\downarrow\rangle - |\downarrow\uparrow\rangle)\]This state is not a product state—it can't be written as \(|\psi_A\rangle \otimes |\psi_B\rangle\).
Perfect Correlations
Measuring spin along any axis:
- If A is up, B is down (and vice versa)
- Results are random (50/50)
- But always perfectly anti-correlated
The EPR Paradox
Einstein, Podolsky, and Rosen (1935) argued this implies:
- Either quantum mechanics is incomplete (hidden variables exist)
- Or there's instantaneous influence between distant particles
They preferred hidden variables. Quantum mechanics disagreed.
The Quantum Connection
Entanglement is now understood as a resource for quantum information processing. It enables quantum teleportation, superdense coding, and is essential for quantum computing. Despite the "spooky" correlations, no information travels faster than light—you can't use entanglement alone for communication.