Now that we have learned about the Born Rule, we are able to study the measurements and how they affect a quantum state.

Arjen helps us understand how a projective quantum measurement can be expressed in the braket notation. This is done by the measurement operators, which let us know the probability of measuring a certain state and the remaining state after performing such a measurement.

Main Takeaways

• The sandwich rule calculates the probability or expectation value of a certain measurement. The latter is the inner product of the initial state and the state resulting from the measurement.
• The identity rule states that the sum over all measurement operators in a basis is the identity matrix.
• The normalization rule expresses that after applying a measurement operator on a quantum state, this needs to be divided by the square root of the probability of such measurement to normalize it.