After having a discussion with a quantum computing colleague, a question came up: is there any meaningful way to measure entanglement (or something related to it) in a solid-state many body system where you don't have the luxury of individual qubit control? Specifically, I am interested in the case of the solid-state, not cold atoms where you can do quite marvelous things at the single qubit level. I suppose there might be various entanglement witnesses out there, but I am wondering which among them is (in-principle) measurable in a real-life solid-state experiment.
To explain what I mean by "meaningful", please not that, as the comments indicate, I acknowledge that measuring the true degree of entanglement of a solid-state system is extremely difficult for fundamental reasons. It is near impossible to put a physical cat into a superposition of two states, for example. However, I would contend that in solid-state systems one is only interested in low-energy phenomena, so entanglement is only of interest for a small subset of the total degrees of freedom. For example, core electrons make up the majority of the degrees of freedom in a solid, but play almost no role in most properties. On the other hand, valence electrons are much fewer in number, but dictate most of the interesting chemical and physical properties. So, by "meaningful" measure of entanglement, I mean a method which allows you to ignore the inactive degrees of freedom that don't contribute anything to the physics of the solid-state system of interest.
As an example of the use of such an entanglement measurable, quantum phase transitions are quite interesting in the context of solid-state systems, and are thought to give rise to enormous entanglement among degrees of freedom as one nears the critical point. If one had an experimentally measurable quantity describing the entanglement, one should be able to identify one of the key properties of quantum phase transitions.
A somewhat related question that I posted several years ago about Quantum Fisher Information https://physics.stackexchange.com/questions/274891/interpreting-the-quantum-fisher-information
