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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

Measurement operators

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

 

Prerequisite knowledge

Further thinking

What is the probability of obtaining the result |0> when measuring the following state?

Solutions

Further reading

For a more advanced view on measurement operators see section 1.8 and 1.9 in N. D. Mermin, ‘Quantum Computer Science: An Introduction’ and section 2.2.3 of M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, 10th anniversary ed. Cambridge ; New York: Cambridge University Press, 2010.