What is ''faithful measurement'' in Quantum Mechanics exactly. I have seen this expression in Kochen-Specker Theorem.
In this case "subquantum element" is a supposed "hidden value".For such more general theories the KS theorem is applicable only if the measurement is assumed to be a faithful one, in the sense that there is a deterministic relation between a subquantum element of physical reality and the value of the observable found on measurement.
To quote wiki (http://en.wikipedia.org/wiki/Kochen–Specker_theorem:
In this case "subquantum element" is a supposed "hidden value".