Entanglement in Algorithms
Most algorithms in quantum computing find their strength in making use of entanglement.
I am interested in evaluating the amount of entanglement generated within an algorithm, maybe even being able to think of knowing how this information changes for different numbers of runs of the algorithm or if the algorithm is run on different numbers of qubits.
How would one best do this?
My thoughts are to calculate the density matrix of the computational qubits at every time step and to find the von Neumann entropy of this multipartite state and work from there but it appears that there are many different kinds of entanglement measures useful for different kinds of situations .
Take Shor's factoring algorithm for example. How would you go about calculating the entanglement at each time step? I have found two approaches thus far,  which takes into account mixed states using the notion of a Groverian measure and  which makes use of standard von Neumann entropy.