In the First International Congress of Basic Science held in 2023, David Mumford gave the opening plenary lecture on Consciousness, robots and DNA. When he discussed on DNA being a measuring instrument opening a Pandora's box, he asked

whether there are "Approximate Macroscopic Unique" states in quantum measurements. Let $T_1, T_2,...,T_n$ be $n$-tuple of selfadjoint operators on an infinite dimensional Hilbert space $H.$ We show that when the commutators are sufficiently small, there are indeed AMU states for the $n$-tuple observables. This is achieved under the circumstance for which the $n$-tuple may not be approximated by commuting ones.