Definition of conditional Fisher information-estimating hidden parameter of probe state through environmental memory
School of Electronic and Communication Engineering, Guiyang University, 550005, Guiyang, Guizhou, China
Accepted: 3 July 2021
Published online: 8 July 2021
Caused by the quantum decoherence of probe system, some state parameters of the probe system are lost after long-time evolution. An indirect estimation scheme is provided to estimate the lost probe parameter through the environmental memory. The results show that the lost probe parameter is indeed hidden in the environment. By the uses of two sets of measurements, one can first project the environmental state to the states containing the most information of state parameters and then collect the information by the probe system. After knowing the results of the first measurement, the hidden parameter can be estimated with the help of the projected environmental state. Conditional Fisher information is defined to determine the precision of the indirect estimation scheme with two sets of measurements. Different from the traditional optimal measurement chosen in direct estimation scheme with a single measurement, the optimal measurements here are chosen as a complete set of projectors based on the equal weight superpositions of the preferred joint states to maximally transmit information through the environment. The present indirect estimation scheme shows advantages in identifying the initial probe state after long-evolution time. Particularly, environmental memory degree shows limit on the precision of estimation through environmental memory.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021