Measurement

The Born Rule

When we measure a qubit, the superposition collapses to either $|0 angle$ or $|1 angle$. The probabilities are given by the Born rule:

• $P(|0 angle) = |alpha|^2$
• P(|1 angle) = |eta|^2

For the $|0 angle$ state [1.0, 0.0]: $P(0) = 1$, $P(1) = 0$ — certain outcome.

For the equal superposition left[rac{1}{sqrt{2}}, rac{1}{sqrt{2}} ight]: $P(0) = 0.5$, $P(1) = 0.5$ — truly random.

import math

def prob_zero(state):
    return state[0] ** 2

def prob_one(state):
    return state[1] ** 2

s = 1 / math.sqrt(2)
superposition = [s, s]

print(round(prob_zero(superposition), 4))  # 0.5
print(round(prob_one(superposition), 4))   # 0.5

After measurement, the qubit is irreversibly in the measured state — the superposition is gone.

Your Task

Implement prob_zero(state) and prob_one(state) using the Born rule.