Unitary Evolution · F2
t = 0.00 |ψ⟩ = |0⟩ norm = 1.0000 ✓
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What happens when time passes?
Move the time slider. Watch the quantum state evolve.
Time t = 0
0
π/2
π
3π/2
2π
Setup
State
Discover
Reflect
Initial State
Rotation Axis
Choose which direction the state evolves on the Bloch sphere.
what to discover Move the time slider slowly. Does the state jump between values — or does it change continuously? Try different initial states and axes. The state always stays on the Bloch sphere surface.
State vector |ψ(t)⟩
|ψ⟩ = 1|0⟩
Measurement Probabilities
|0⟩
100%
|1⟩
0%
Relative Phase
φ between |0⟩ and |1⟩
—
Bloch azimuth
= φ
|α|² + |β|² = 1.0000 ✓
watch continuously Every quantity updates smoothly as time passes. The state never jumps. Normalization never changes. This is the signature of unitary evolution — information-preserving, continuous, reversible.
Before you move the slider: does the quantum state change in jumps or continuously?

The state changed continuously. Every point along the slider is a valid quantum state. There are no jumps, no discrete steps.

This is a fundamental property: quantum evolution is continuous.

|α|² + |β|² stayed exactly 1.000 throughout the entire evolution — no matter how the state changed.

Evolution preserves total probability. Information is not destroyed — it is rearranged.

The evolution is perfectly reversible. Dragging the slider backward retraces the exact same path.

No information was lost. This is what makes quantum evolution unitary — it has a perfect inverse.

Measurement is irreversible. The state collapses to one outcome — all the other amplitude information is gone.

Evolution ↔ reversible, information-preserving.
Measurement ↔ irreversible, information-extracting.

These are the two fundamentally different things that happen to a quantum state.

R1
What stayed constant during the entire evolution? What does that tell you about information?
R2
Did the state change continuously or in jumps? What evidence did you see?
R3
What changed when you switched from X to Y to Z axis? What stayed the same?
R4
You reversed the slider and the state retraced its path. Could you do the same thing after a measurement?
R5 ★
What is the key difference between quantum evolution and quantum measurement?
Core Understanding

Quantum systems never stand still. An isolated quantum state evolves continuously, preserving all information, and can be perfectly reversed. This is fundamentally different from measurement — which extracts classical information at the cost of destroying the quantum state.