Misconceptions/Foundations/The no-cloning theorem
IntermediateFoundations5 minInteractive

The myth

You can copy a quantum state just like copying a classical bit

01

Why people believe this

Copying information is fundamental to classical computing — RAM, cache, registers all copy bits constantly. Quantum computers store information in qubits, so copying qubit states should work the same way.

02

The correction

The no-cloning theorem (Wootters and Zurek, 1982) proves that it is physically impossible to create a perfect copy of an unknown quantum state. This follows directly from the linearity of quantum mechanics. If a cloning machine could copy |0> and |1>, linearity requires it to map (|0> + |1>)/sqrt(2) to a product of two copies — but that product state is not the same as the entangled state the linearity would produce. No-cloning is not a hardware limitation — it is a law of physics with deep implications for quantum error correction and cryptography.

03

Try it in the simulator

What to do

Try to build a circuit that copies q0 to q1 — starting from |00> make q1 match q0 for any input state. You will find CNOT copies |0> to |0> and |1> to |1> but fails for superposition states. Load Bell state and notice the output is an entangled state, not two identical copies of q0.

Open in simulator
04

Research notes

Tags

#no-cloning#quantum information#error correction#QKD#linearity

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