QUANTUM 02
Amplitudes, collapse, interference, and measurement bases
Sinclair College - Dr. Mike Libassi
TODAY
01 · AMPLITUDES
A qubit with both amplitudes nonzero is in superposition. It isn't secretly 0 or 1; the amplitudes set the odds of each answer.
The number attached to each basis state. It can be positive, negative, or complex.
Probability = |amplitude|². −0.707 gives the same 50% as +0.707.
All squared amplitudes add up to exactly 1.
01 · AMPLITUDES
The minus sign is invisible to a 0-or-1 measurement, but it completely changes what happens after the next gate.
02 · COLLAPSE
A qubit in superposition, e.g. 50/50
A random result, weighted by |amplitude|²
The state becomes |0⟩ or |1⟩
Same answer every time; the blend is gone
The original amplitudes cannot be recovered from that qubit. You need many identically prepared qubits to estimate them.
03 · INTERFERENCE
Peek in the middle and the superposition collapses. The interference disappears and the result becomes a 50/50 coin flip.
04 · BASES
Asks "0 or 1?" Distinguishes |0⟩ from |1⟩ perfectly.
Asks "+ or −?" Apply H, then measure. Distinguishes |+⟩ from |−⟩ perfectly.
A state that is certain in one basis is a pure coin flip in the other.
This two-basis idea is the foundation of BB84 quantum key distribution (Quantum 07).
SECURITY CONNECTION
Reading a quantum message changes it.
WRAP-UP
Superposition means both amplitudes are nonzero; probabilities are |amplitude|²
Measurement gives a random result and the qubit collapses to it
Amplitudes can be negative, so paths can cancel: that's interference
Measuring in the wrong basis gives noise, the basis of quantum security
DISCUSSION
Why would an algorithm designer want amplitudes that can be negative?
Think about what happens to wrong answers when their paths carry opposite signs.