Equivalence classes and generalized coherent states in quantum measurement

Summary

The notion of an equivalence class, which was first considered by Jauch, is introduced into generalized coherent-state formalism in quantum measurement. Two equivalent states in Jauch’s treatment cannot be distinguished by measurement of any observables of a physical system (the definition of an observable also being ambiguous). In our approach it is possible in principle, but becomes more difficult asN→∞,N being the number of molecules constructing a detector; we cannot distinguish them at all in the large-N limit. Two models are presented, which show that the notion of equivalence class is well suited to the generalized coherentstate approach. It is also shown that in each model a statistical operator and its mixed-state part belong to the same equivalence class.