There Exist Nonorthogonal Quantum Measurements that are Perfectly Repeatable
Francesco Buscemi, Giacomo Mauro D’Ariano, Paolo Perinotti · Physical Review Letters · 2004
We show that, contrary to the widespread belief, in quantum mechanics repeatable measurements are not necessarily described by orthogonal projectors--the customary paradigm of observable. Nonorthogonal repeatability, however, occurs only for infinite dimensions. We also show that, when a nonorthogonal repeatable measurement is performed, the measured system retains some "memory" of the number of times that the measurement has been performed.