The Mechanics Of Quantum Measurements

Learn about the Observable

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In the previous post, we learned that the quantum superposition inevitably collapses when you look at it. It collapses to one of the basis states of your computational basis. This is usually the vertical direction of the qubit.

There is, of course, nothing special about the vertical direction. The definition of a qubit’s computational basis is entirely arbitrary.

For example, we can rotate the magnets through 90°. The measurement apparatus will still deflect the atom in the direction of the electron’s spin. Consequently, the atoms now behave as magnets with their north and south poles aligned in the horizontal direction, as is depicted in the following figure.

Image by author

There is no rule telling us to look at a quantum mechanical system from a certain perspective. We could define any two (for a two-dimensional system) opposing points and ask for the probabilities of measuring the system as either one. Opposing here means that these points are orthogonal to each other and their outcomes, therefore, are mutually exclusive. Of course, if we have an 𝑛-dimensional system, we would need to use 𝑛 points — the basis states. We can…