Observability of relative phases of macroscopic quantum states

Abstract

After a measurement, to observe the relative phases of macroscopically distinguishable states we have to ``undo'' a quantum measurement. We generalise an earlier model of Peres from two state to N-state quantum system undergoing measurement process and discuss the issue of observing relative phases of different branches. We derive an inequality which is satisfied by the relative phases of macroscopically distinguishable states and consequently any desired relative phases can not be observed in interference setups. The principle of macroscopic complementarity is invoked that might be at ease with the macroscopic world. We illustrate the idea of limit on phase observability in Stern-Gerlach measurements and the implications are discussed.