Asymptotic Theory of Quantum Channel Estimation

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 various types upper bounds QFI, but they were proven achievable only several specific situations. It was known arbitrary grows either linearly or quadratically with N. Here we show simple criterion can determine whether scaling linear quadratic. both cases, error correction protocol achieve it computable via semidefinite program. When quadratic, Heisenberg limit, feature noiseless channels, recovered. linear, still general larger than times single-channel and, furthermore, sequential estimation strategies provide no advantage parallel ones.Received 23 March 2020Revised 20 December 2020Accepted 26 February 2021DOI:https://doi.org/10.1103/PRXQuantum.2.010343Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasQuantum correctionQuantum metrologyQuantum sensingQuantum Information