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TWO QUBITS
Two qubits, one shared state
Four amplitudes
|00⟩, |01⟩, |10⟩ and |11⟩.
Not entangled
The state splits into 'A's state' times 'B's state'.
Entangled
It can't be split: only the pair has a state.
Entanglement is a property of the whole, not of the parts.
THE RECIPE
Making a Bell pair
H
Puts qubit A in an equal blend.
CNOT
Flips B only when A is 1.
Result
(|00⟩ + |11⟩)/√2: always 00 or 11.
Two gates are enough to entangle two qubits.
MATCHING RESULTS
Perfectly linked, perfectly random
Each qubit alone
Gives 0 or 1 at random.
The pair
Always agrees, however far apart.
No messages
Because each side looks random, nothing can be sent faster than light.
Linked results, but no signal: that's entanglement.
THE BELL TEST
Stronger than any classical link
The question
Could the particles just carry hidden instructions?
The test
Measure at different angles and compute a score S.
The answer
Hidden instructions give at most 2; nature reaches about 2.83.
Experiments confirming this won the 2022 Nobel Prize in Physics.
WHY IT MATTERS
Computers need entanglement
Power
Without entanglement a quantum computer is no better than a classical one.
Error correction
Spreads one qubit's information across many entangled qubits.
Fragility
Entanglement is easily destroyed, and it can spread errors too.
Next: how interference turns all this into answers.
UNIT 6 STUDY COMPLETE
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Ready for the Fab Challenge?
You've built a Bell pair, measured its matching results and beaten the classical limit.