# Quantum Measurements: The Average value is the cosine

Gold Member

## Homework Statement

We know: In a measurement of quantum mechanics (basic) the average value is the cosine of the angle between the orthonormal basis of the measurement apparatus and the qubit (vector) entering it.

Question: How do we prove this?

## The Attempt at a Solution

Can there be a mathematical proof to this? Or is this done by painstaking experiments in a laboratory?

If you can answer this question, then I will know how to proceed.

Thank you.

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mfb
Mentor
You first need a description of the measurement setup and the definition of the angle and so on.
Once you have that in the way the problem statement needs it, you can write your measured state as superposition of the eigenstates of the measurement, and the cosine will become part of the amplitude. The relation between amplitude and "probability" is an experimental result, but it is possible to show that all other relations would lead to very odd results.

• RJLiberator
Gold Member
Thank you for your reply. That helps out (writing an essay on this topic).