Quantum hypothesis testing in many-body systems

One of the key tasks in physics is to perform measurements order determine state a system. Often, are aimed at determining values physical parameters, but one can also ask simpler questions, such as ``is system A or B?''. In quantum mechanics, latter type be studied and optimized using framework hypothesis testing. many cases explicitly find optimal measurement limit where has simultaneous access large number n identical copies system, estimate expected error becomes large. Interestingly, estimates turn out involve various information theoretic quantities relative entropy, thereby giving these operational meaning. this paper we consider application testing many-body systems field theory. We review some necessary background material, study detail situation two states wants distinguish parametrically close. The relevant variance for which prove new inequality. explore strategy spin chains two-dimensional conformal theory, focusing on task distinguishing reduced density matrices subsystems. turns somewhat cumbersome implement practice, discuss possible alternative corresponding errors.