What quantum measurement formalism is easiest to implement physically? As part of my studies and research, I have learned to work with three different measurement formalism which I define to avoid any ambiguity with the nomenclature: 


*

*General measurements, which are described by a collection of self-adjoint operators $\{M_m\}_m$ satisfying $\sum_m M_m^\dagger M_m= I$. 

*POVMs, which are described by a collection of positive semi-definite operators $\{E_m\}_m$ satisfying $\sum_m E_m = I$. 

*Projective measurements, which are described by a collection of positive semi-definite operators $\{P_m\}_m$ satisfying $\sum_m P_m= I$ and $P_m P_{m'}= \delta_{m,m'}P_m$.


As I am from a theoretical computer science background, I have but a limited understanding of the physical implementation of quantum measurements. I know that all three formalism are equivalent by using ancilla states and unitary evolution, however this could be hard to realise on a physical implementation of a quantum system. My question therefore is: 

Is there a measurement formalism that is (in general) easier to realise across all known physical implementation of quantum states?  

My intuition leads me to believe that projective measurements are the simplest to implement as they are they are a special case of the other two (when no ancilla is available), but this intuition might be flawed. As mentionned in Nielsen and Chuang, projective measurements are non-destructive, but there are measurement devices that destroy the state in the process of measuring it. 
A maybe easier question, but one to which the answer would still satisfy me would be: what kind of measurement operator (i.e. formalism 1, 2 or 3) are being realised by devices that measure qubit systems.
 A: My favorite is the unitary measurement formalism based on Stinespring dilation theorem, which was introduced here for qubits and here in general. I've also summarized this measurement formalism in my answers here, here, and here. This representation is equivalent to the Kraus / CPTP formulations by Choi's Theorem (which definitely includes the 1st and 2nd case you mention).
The formalism discussed in the links corresponds to strong / projective measurements. For weak measurements, generalized measurements, and continuous measurements (e.g., where you have to "wait" to ensure you've had a chance to collect any photons), I am partial to the von Neumann "pointer-particle" formulation, which is described in these notes. The von Neumann version is Hamiltonian, while the projective version mentioned above is unitary. In the limit that we implement the von Neumann Hamiltonian very quickly, the corresponding unitary will agree with the projective measurement version.
Which version is relevant depends on the particulars of the experiment. For trapped ions, e.g., measurements can be very close to projective. This also holds in some ultra-cold atomic gases I believe. In cavity QED systems coupled to atoms, people use the von Neumann version fairly directly to describe the continuous measurement of photons that escape the cavity.
I've never used POVMs and I don't really know how to do so, or how they differ from the CPTP version.
