beginner · Interactive lab
No-cloning
The obvious copier — measure it, then make two of what you saw — copies |0⟩ and |1⟩ perfectly and quietly destroys anything else. No better device exists: copying an arbitrary unknown state is ruled out by a theorem.
By the end: Tell copying apart from measure-and-prepare, and see why agreeing copies are not faithful copies.
Your challenge
Start here. This lab opens with every claim marked as shown by the bench, which is the wrong starting point twice over: two of these claims the bench actually refutes, two are ruled out by a theorem no number of trials could establish, and one is about a real device. Reaching for the theorem, or for "this bench cannot say", on a row whose experiment has already been run is the other wrong answer, and it is graded as one. Read each row and judge it.
See it happen
A copier that works, until it does not
- Preparation → The bench
- The bench → The copier
- The copier → Measurement
- Measurement → Tally
A copier on the bench
The copier does the obvious thing: Measurement in the Z basis, then prepare two copies of whatever came back. Watch it on a state it was built for.
Learn more
Why this pattern exists
Every engineer's instinct with fragile state is to copy it: take a snapshot before the risky operation, keep a replica, retry from the copy if something goes wrong. For a qubit in an unknown state, none of that is available, and the reason is not that the hardware is immature. Put the obvious copier on the bench — it measures the qubit in the Z basis and prepares two copies of whatever it saw — and watch it work perfectly on |0⟩ and on |1⟩. Then send |+⟩ through it. The two copies agree with each other every time, which is what makes the trick so convincing, and they are both the wrong state: read them in the X basis and the certainty |+⟩ had is gone. No amount of better engineering fixes that, because copying an arbitrary unknown state would break the linearity the whole theory is built on.
The bench from the previous lesson, with a copier in the middle: it measures whatever arrives in the Z basis and prepares two copies of what it saw. Both copies are then read in a basis you choose. Every graded experiment runs on a fixed seed.
- Tell copying apart from measure-and-prepare, and see why agreeing copies are not faithful copies.
- Say which claims a bench can settle, which are ruled out by a theorem, and which belong to a real device.
- Name the engineering consequences: no snapshots, no replay of an unknown state, and why an eavesdropper cannot go unnoticed.
The rule this lesson applies: The no-cloning theorem says there is no operation that takes an arbitrary unknown state and produces two of it. The proof is a few lines of linear algebra, and its consequences are practical. There is no snapshot to roll back to, so error correction spreads information across many physical qubits rather than duplicating one. There is no replay: a retry has to re-run the preparation, not resend the state. And an eavesdropper cannot take a quiet copy of a key in flight — any attempt has to measure, and measuring in the wrong basis disturbs what arrives, which is what quantum key distribution turns into a detector. Note what is not claimed: known states can be prepared again as often as you like, and classical information can always be copied. The restriction is precisely on the unknown. This bench computes the statistics the standard model predicts; it models no noise, no decoherence and no hardware, and it cannot prove a theorem — it can only show you a copier failing, which is a different thing and is marked as such on the rows.