|+⟩ state
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What to notice
The state points halfway between |0⟩ and |1⟩, so both outcomes are equally likely.
Quantum state laboratory
Quantum Superposition
Prepare a qubit, see its state as a direction in 3D, and test how probabilities become measurement results.
1Prepare2Predict3Measure
Step 1
Prepare the qubit
Choose a familiar state or create your own using the two angles.
0° · |0⟩180° · |1⟩
0°360°
One direction, two amplitudes
0.707|0⟩ + (0.707 + 0.000i)|1⟩
The amplitudes can be complex. Their squared magnitudes—not the amplitudes themselves—give measurement probabilities.
Z-basis prediction
50 / 50
Outcome probabilities
Measure |0⟩50.0%
Measure |1⟩50.0%
Try thisMove only φ. The arrow rotates, but these two probabilities stay the same.
Step 3
Measure many identical qubits
Every dot is one newly prepared copy of the same state. Individual outcomes are random; the overall pattern follows the probabilities above.
Experiment resultReady to measure
0 trials
0|0⟩
0|1⟩
Measurement outcomes will appear here.
Reflect
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Why does one measurement never show a superposition?
A state can contain both amplitudes, but a Z-basis measurement returns one definite outcome. Evidence for the prepared state appears in statistics collected from many identically prepared qubits.