Measuring a qubit is asking it a yes/no question. The qubit gives back one of two outcomes, but only after you decide which question to ask, by picking an axis on the Bloch sphere.
The probability of each outcome is set by where the state vector currently points relative to that axis. After the measurement, the state collapses to align with the outcome you got.
Pick a basis, get an outcome
In the interactive above, click Measure Z first. You'll get either |0⟩ or |1⟩, with probabilities determined by the vector's alignment with the z-axis. The state then snaps to one of the two poles.
Now reset and click Measure X. The same starting state can give a completely different answer, because you're asking a different question.
The Born rule
The probability of each outcome follows a clean rule. For any axis you measure along, the probability of getting the +axis outcome is:
where α is the angle between the state vector and the +axis direction.
When the state points exactly along the +axis, α = 0, so P(+) = 1, guaranteed outcome. When it points at the −axis, α = 180°, so P(+) = 0. On the equator (perpendicular to the axis), α = 90° and P(+) = ½, a fair coin flip.
This is the Born rule, named for Max Born who introduced it in 1926. It's where probability enters quantum mechanics.
Collapse, and why it matters
After a measurement, the state has changed: the vector now points to whichever pole gave you the outcome. Measure again on the same axis and you'll get the same answer. The qubit has "snapped" to that pole.
This is what people mean by wave-function collapse. It's the one operation in quantum mechanics that isn't reversible. No quantum gate can undo a measurement.
For algorithms, this matters because measurement is also when information leaves the quantum world. Inside the circuit, qubits sit in superposition and gates rotate them. At the end, you measure to read out an answer. and once you do, the quantum advantage is gone.
Related concepts
- What is a quantum gate? The reversible operations that run before measurement.
- Hadamard gate: the gate that creates a state with 50/50 measurement outcomes.
- Pauli gates: these can be measured as observables, not just applied as gates.
- The Bloch sphere: the visualization that makes measurement intuitive.
Frequently asked questions
What does it mean to measure a qubit?
Measurement is asking the qubit a yes/no question. You pick an axis on the Bloch sphere (typically the z-axis), and the qubit gives back one of two outcomes corresponding to the two poles of that axis. The probability of each outcome is set by how aligned the qubit's state vector is with the axis.
Why does measurement collapse the state?
Once the qubit gives you an outcome, its state aligns with the pole that produced that outcome. If you measure again on the same axis, you'll always get the same answer. This is called collapse, or projective measurement. It's irreversible: there's no quantum gate that can undo a measurement.
What's the Born rule?
The Born rule is the formula that gives you the probability of each measurement outcome. For a qubit, the probability of the +axis outcome is cos²(α/2), where α is the angle between the state vector and the axis. Named after Max Born, who introduced it in 1926.
Can you measure a qubit without collapsing it?
Generally no. Projective measurement always collapses the state. There are softer schemes called weak measurements that disturb the state less, but they also extract less information. There's a fundamental tradeoff between how much you learn and how much the state changes.
What does it mean to measure in different bases?
Every axis through the Bloch sphere defines a measurement basis. The standard z-basis gives you |0⟩ or |1⟩. The x-basis gives |+⟩ or |−⟩. The y-basis gives |+i⟩ or |−i⟩. Choosing a basis is choosing which question to ask the qubit.
Why is measurement irreversible if every quantum gate is reversible?
Measurement isn't a gate. Gates are unitary operations the algorithm runs internally. Measurement is the moment information leaves the quantum system and enters the classical world (your readout, your screen). That irreversibility is fundamental: it's where probability enters quantum mechanics.
Get Qubi
Measure a qubit with your hands.
Qubi shows the full superposition until you press measure, then it collapses, just like a real qubit. Measure on any axis. Watch the probability play out.