Quantum Mechanics · Chapter 18

Entanglement and nonlocality

States of two systems that are not states of each. The Bell states, the argument of Einstein, Podolsky and Rosen, the correlations of the singlet, Bell’s inequality and the experiments that break it, why entanglement still cannot send a message or be copied, and how much of it a state holds.

∣ Φ^{+} ⟩ = \frac{∣ 00 ⟩ + ∣ 11 ⟩}{2}

ρ^_{A} = tr_{B} ρ^_{A B}

S (ρ) = - tr (ρ lo g ρ)

∣ S_{CHSH} ∣ \leq 2

Lessons

Build the foundation

Bell’s inequalityBell asked what any local theory with pre-set answers must obey.

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06No signalling and no cloningIf measuring $A$ at once changes what can be predicted about $B$, can $A$ send $B$ a message?Read lesson →

07Measuring entanglementHow much entanglement does a state hold?Read lesson →

08Chapter practiceBring the chapter together: entangled states and the Bell basis, the EPR argument, the singlet correlation, Bell’s inequality, no signalling and no cloning, and the measures of entanglement. No worked example sits above the answers.Read lesson →

Mapping the lesson.

Entanglement and nonlocality

Build the foundation