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Measurement — why you only ever see 0 or 1

A qubit holds a rich continuous state, yet measuring it always yields a plain 0 or 1 — and destroys the superposition. This collapse is quantum computing's central constraint.

FoundationsQuantum Computing~11 min

Before this lesson

  • Lesson: From bits to qubits

A qubit in superposition carries a continuous, information-rich state — two amplitudes with magnitude and phase. So it is a shock that when you measure it, you get back just a single classical bit: 0 or 1. All that structure collapses to one of two answers. Understanding this rule is understanding both the power and the frustration of quantum computing.

The Born rule

Measurement is probabilistic, and the probabilities are fixed by the amplitudes:

P(measure 0) = |α|²        P(measure 1) = |β|²

This is the Born rule. You never observe α or β; you only ever observe an outcome, drawn with these odds. Run the identical qubit a thousand times and you can estimate the probabilities from the tally — but any single measurement is just one 0 or one 1.

Collapse is irreversible

Measurement does more than reveal a value — it changes the qubit. Before, the qubit was α|0⟩ + β|1⟩; the instant you measure and see 0, the state becomes simply |0⟩. The superposition is gone, and re-measuring now gives 0 every time. The other possibility has been erased. There is no peeking: you cannot look at a qubit without collapsing it.

Why this shapes everything

This one rule dictates how quantum algorithms must be built:

  • You get one shot to read out. A computation might place many possibilities in superposition, but a single measurement returns only one of them, at random by the Born rule. Naively, that is no better than guessing.
  • So the algorithm must bias the odds. The real work — using interference (from the phase you met last lesson) — is to make the useful answer's amplitude large and the useless answers' amplitudes small, so that when you finally measure, the right answer is overwhelmingly likely.
  • You often repeat and aggregate. Many quantum algorithms run several times and take the most common or a verifiable result.

That is the quantum bargain: enormous parallel structure inside the state, but a narrow, probabilistic, one-time readout. Everything clever in the field is about winning that bargain. And it gets stranger still when two qubits share a state — entanglement, next.

Key takeaways

  • Measuring a qubit yields 0 or 1 with probabilities |α|² and |β|² — the Born rule — never the amplitudes themselves.
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  • Because you can't read the amplitudes directly, quantum algorithms must arrange for the right answer to be the likely measurement.

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