A quantum particle on the real line R has as configuration space this real line R, while its state space is the infinite dimensional complex Hilbert space of square integrable complex valued functions on R. In Quantum Information, a fundamental role is played by finite dimensional complex Hilbert spaces. Typically, they are the state spaces of finite sets of qubits. Question : what is the configuration space corresponding to such a finite dimensional complex Hilbert space ? Related question : what are the position and momentum operators on a finite dimensional complex Hilbert space ?

ifsomeone (like the OP) wants to use "configuration space" in this context then isshouldhave this meaning? – Andreas Blass Jun 14 '12 at 13:34