Measurement replaces the amplitudes

Measure a qubit in the computational basis, the usual arrangement that distinguishes 0 from 1, and the apparatus returns one of those two values. The chances were fixed a moment earlier by the squares of the amplitudes. In the ideal measurement this note uses, the qubit is left in the state you just read, with an amplitude of 1 on that outcome and 0 on the other, so a second reading done at once in the same arrangement repeats the first.

Bring a fresh copy if you want another toss from the same preparation. The copy you just measured now holds only the state it gave you, and the old amplitudes are gone from it.

Keith called the click a look at the answer. Malcolm called it a new physical event, because the apparatus becomes entangled with the qubit, which is a way of saying the two now share one joint description in which the reading and the qubit match. You do not receive the amplitudes on a slip of paper. You receive one bit, and the joint description is why the immediate repeat agrees with the first click.

A story often goes round in which the qubit holds both values until a person stares and the state collapses. The laboratory account does not need a person in the room. A photodiode or a resonator will do. What counts is that the result leaves a lasting mark in the apparatus, whether or not anyone reads it.

Each new copy is a toss whose bias the squared amplitudes fix, and the tosses do not remember one another. A few dozen shots estimate the chances, and averaging those shots does not bring the signs back, because a single click in this arrangement never reported a sign in the first place. Checking a sign takes another gate, one that turns the sign into a difference of chances, after which a measurement can see it. On this site that gate is the Hadamard, and the sign itself is written with Z.