Can everything be copied?
Work through three cases. Notice what changes each time.
A — Classical information
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copy
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B — Known quantum state
|0⟩
|1⟩
|+⟩
|−⟩
Select a state above
This is not cloning
This works because you know the state. The second qubit was prepared from its classical description, not by copying the quantum state itself. Preparation from a known description is always possible.
C — Unknown quantum state
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Someone prepared this qubit in a state you do not know. It could be any point on the Bloch sphere.
Let's go deeper
Can you build a machine that copies every possible quantum state? Switch to Tab 2 to find out.
Build your own cloning machine
Suppose a machine U can clone every quantum state. Let's test it.
Step 1 — Test basis states

The machine takes a state and a blank qubit |0⟩. It should output two identical copies. (Inside, it is a CNOT gate: it flips the blank qubit when the first one is |1⟩.)

U(|0⟩|0⟩)
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U(|1⟩|0⟩)
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How real experiments work
You cannot learn a state from one particle, and you cannot copy it. Here is what physicists actually do.
One electron spin in a mystery state
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Sandbox
Experiment freely
No instructions. No guided path. Only experimentation.
⚠ Important — What you're observing
When you select |0⟩ or |1⟩, the simulation shows successful copying because this quantum operation has been designed to copy that particular orthogonal pair of basis states. This may give the impression that only superposition states are problematic, but that is not the full picture.
The no-cloning theorem is about universality: there is no single quantum operation that can correctly copy every possible unknown quantum state. When a qubit arrives, it could be |0⟩, |1⟩, |+⟩, or any other superposition, and the same cloning machine must work regardless of which state is supplied.
Because quantum evolution is linear, applying this same operation to |+⟩ produces the entangled Bell state (|00⟩ + |11⟩) / √2 rather than two independent copies |+⟩|+⟩. This contradiction shows that no universal quantum cloning machine can exist, even though the operation successfully copies the chosen basis states.
State selector
|0⟩
|1⟩
|+⟩
|−⟩
Unknown
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