Superposition and Measurement

Learn more

Why this pattern exists

Three words first, because the rest of the lesson leans on them. A **qubit** is what a quantum computer stores instead of a bit; like a bit, reading one gives you a single symbol back. A **basis** is the question you point the measuring device at — this bench offers two of them, and they have different answers, which is the whole lesson. And **|+⟩** is just a name for one particular preparation of a qubit; say it as "plus", and take it as a label rather than as mathematics. Now the picture to unlearn. Put a fair coin in a box and shake it: it is already heads or tails, and the lid only tells you which. Prepare a qubit in |+⟩ and ask the Z question — the basis whose answers are called 0 and 1 — and it does behave like that coin: about half 0 and half 1, however long you run it. Now ask a different question. Ask in the X basis, whose answers are + and −, and the qubit says + every single time, while the coin still gives you half and half. Two systems that are identical under one question and completely different under another are not the same system. That is what superposition means here, and this bench can show it trial by trial. One habit before you start: these are counts from a finite number of trials. Two hundred tosses of a fair coin do not land on exactly one hundred, and neither do these. Read a tally as "about half" or "every single time", and compare it against what the model predicts — which every row tells you.

A bench with two things on it: a qubit prepared in |+⟩ and a fair coin in a closed box. A measuring device can be pointed at either of them and set to either question — the Z basis, whose answers are 0 and 1, or the X basis, whose answers are + and −. That choice of question is what "basis" means. Every graded experiment runs on a fixed seed, so the numbers never move, and each row says what the model predicts beside what the trials actually gave.

• Tell superposition apart from ignorance: a prepared |+⟩ and a coin in a box differ in a way you can measure.
• Read an outcome distribution as evidence, and say what a single measurement can and cannot tell you.
• Say what a browser simulation of outcome statistics does not settle, and refuse claims that need real hardware.

The rule this lesson applies: A measurement has a basis: the question you decided to ask, chosen before the answer exists. |+⟩ has a definite answer to the X question and no answer at all to the Z question, and a coin in a box has a definite answer to the Z question and none to X. Neither system has answers to both, which is why one copy cannot hand you both — measuring in Z leaves the copy in |0⟩ or |1⟩, and the X certainty that was there is gone. Once measured, a qubit stays measured: ask the same question again and the same answer comes back, which is why nothing here is mystical, only unfamiliar. What a qubit does not do is carry more classical information per readout: one measurement hands back one symbol, and one qubit yields at most one classical bit that way. This page computes the statistics the standard model predicts and draws them; it models no noise, no decoherence and no hardware. Anything that depends on how long a real device holds a state is outside what it can settle, and this lesson grades that distinction rather than leaving it to a disclaimer. It grades the opposite mistake too. "This bench cannot say" is the right answer exactly once here, and reaching for it on a claim whose experiment is sitting on the row is not caution — it is refusing evidence you were given, and it is graded as the same kind of error as overclaiming.