The quantum Fisher information (QFI), as a function of states, measures the amount that state carries about an unknown parameter. (entanglement-assisted) QFI channel is defined to be maximum output assuming entangled input over single probe and ancilla. In metrology, people are interested in calculating N identical copies when N??, which called asymptotic QFI. Over years, researchers found vari...

All rings in this paper are assumed to be commutative with identity, and they will generally also be Noetherian. In several recent papers the asymptotic theory of ideals in Noetherian rings has been introduced and developed. In this new theory the roles played in the standard theory by associated primes, i?-sequences, classical grade, and Cohen-Macaulay rings are played by, respectively, asympt...