# Is there a list of known quantum measurements?

Quantum Measurement can be divided into General Measurements, Projective measurements and general POVMs. And there are also some special kinds of quantum measurements that have their own name, such as :

• adiabatic measurement (protective measurement)
• weak measurement
• quantum nondemolition measurement and so on.

Is there a list of those special kinds of measurements?

• note that "general measurement" and "general POVM" are pretty much the same thing (though in the "general measurement" formalism one often keeps track of/defines post-measurement states). More generally, any measurement can be thought of as a special case of a POVM/general measurement.
– glS
Apr 27 at 10:05
• In the Book of Nielsen and Chuang, they describe them in two sections. But I think it's the reason for writing an easy understanding book. But in box 2.5, they stated "POVMs are best viewed as a special case of the general measurement formalism, providing the simplest means by which one can study general measurement statistics, without the necessity for knowing the post-measurement state." Apr 27 at 10:24
• see also the relevant discussion in quantumcomputing.stackexchange.com/q/12275/55
– glS
Apr 27 at 10:27
• A POVM alone is only able to describe the measurement statistics. To describe post-measurement states, we have to go beyond POVMs and define the actual quantum channel corresponding to the measurement. This is sometimes called a "quantum instrument". Note that many quantum instruments correspond to the same POVM. This is due to the non-uniqueness of a "square root" $M$ for a given effect $E=M^\dagger M$. Apr 27 at 11:55