Speed limit of quantum metrology

Yusef Maleki; Bahram Ahansaz; Alireza Maleki

doi:10.1038/s41598-023-39082-w

Speed limit of quantum metrology

Sci Rep. 2023 Jul 25;13(1):12031. doi: 10.1038/s41598-023-39082-w.

Authors

Yusef Maleki¹, Bahram Ahansaz², Alireza Maleki³

Affiliations

¹ Department of Physics and Astronomy, Texas A&M University, College Station, Texas, USA.
² Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran. bahramahansaz@gmail.com.
³ Department of Physics, Sharif University of Technology, Tehran, Iran.

Abstract

Quantum metrology employs nonclassical systems to improve the sensitivity of measurements. The ultimate limit of this sensitivity is dictated by the quantum Cramér-Rao bound. On the other hand, the quantum speed limit bounds the speed of dynamics of any quantum process. We show that the speed limit of quantum dynamics sets a fundamental bound on the minimum attainable phase estimation error through the quantum Cramér-Rao bound, relating the precision directly to the underlying dynamics of the system. In particular, various metrologically important states are considered, and their dynamical speeds are analyzed. We find that the bound could, in fact, be related to the nonclassicality of quantum states through the Mandel Q parameter.