I got a referee report for a paper submitted to PhysChemChemPhys that looks at the quantum entanglement of electronic and nuclear degrees of freedom in molecules. The paper goes beyond the calculations considered here, and explores subtle issues about how entanglement may or may not be related to the breakdown of the Born Oppenheimer approximation.
One referee asked a good but basic question, "Why is the von Neumann entropy the appropriate measure of entanglement to consider here?"
Here is my answer. I think experts could do better and so I welcome suggestions.
The von Neumann entropy is widely accepted as the best measure of quantum entanglement for pure quantum states defined on bipartite systems, such as that considered here. This is because the von Neumann entropy satisfies certain desired criteria, including vanishing for separable states, monotonicity (it does not increase under local operations or classical communication between the subsystems), additivity, convexity, and continuity.
It was a bit of work to come up with this answer, because this is all second nature to people who work in quantum information. It is hard to find a place where this is clearly stated and discussed in detail. The Quantiki wiki entry on entanglement measures and the axiomatic approach, along with the review article by the Horodecki family helps.
Anyone suggest a place where this basic issue is discussed and worked out in detail?
The big challenge is defining entanglement measures for multi-partite systems and for mixed quantum states.