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Measurement & Born Rule

Quantum measurement collapse and probability statistics

Prepare a qubit in any state by choosing Bloch angles. Select a measurement basis (Z, X, or Y) and perform single or batch measurements. Each measurement collapses the state to a basis eigenstate with Born-rule probability. Watch the empirical frequencies converge to the theoretical values as you accumulate data.

Prepare State

statebasis axis

Measurement Basis

Born rule: p(+1)=∣⟨+∣ψ⟩∣2=0.7500p(+1) = |\langle +|\psi\rangle|^2 = 0.7500
Born rule: p(−1)=∣⟨−∣ψ⟩∣2=0.2500p(-1) = |\langle -|\psi\rangle|^2 = 0.2500
+1-10.00.20.40.60.81.0probabilityexpected (Born rule)observed frequency

Each measurement collapses the state onto a basis eigenstate with probability given by the Born rule. As trials accumulate, empirical frequencies converge to the theoretical probabilities.

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Measurement & Born Rule — Quantum Foundations Labs · hbar.university