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Fundamentals

01 /Quantum computers with magical advantage? 02 /Bra-ket notation 03 /Born rule 04 /Bloch sphere 05 /Measurement operators 06 /Experimental and theoretical measurements 07 /How to measure in any basis 08 /State decomposition 09 /Why every maximally entangled state is secretly a Bell state 10 /Coherence 11 /Relaxation 12 /Quantum materials: the environment of a qubit 13 /Introduction to quantum error correction (QEC) 14 /Multiqubit systems 15 /Multiqubit gates 16 /Entanglement 17 /Measuring multiqubit systems 18 /Superdense coding 19 /Teleportation 20 /Entanglement swapping

Born rule

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.

Prerequisite knowledge

Further thinking

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?

Solutions

Further reading

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/.