Making use of the famous Schrödinger’s cat, Arjen Vaartjes (QuTech) presents to us the concepts of normalization and quantum probabilities, and how together they can help us understand the Born Rule. The Born Rule is a mathematical trick that helps us know how likely the possible outcomes are when we measure a qubit.
This is a widely used trick for any study of the mathematics of a quantum measurement.
- Bra-ket notation
- Basic linear algebra
You are given an experimental set-up with an electron that can either occupy a quantum state or not occupy it. Which state represents the electron if you know the probability of occupying the state is 0.25?
What is the state of the electron if now you know the probability of occupying the state is 0.1?
For a more advanced view on the Born rule see section 1.8 and 1.9 in N. D. Mermin, ‘Quantum Computer Science: An Introduction’.
For a historical background on the derivation of the Born rule see https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/.