Dynamical phase transitions as a resource for quantum enhanced metrology

Understand

We consider the general problem of estimating an unknown control parameter of an open quantum system.

• We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated.
• We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf.
• "Heisenberg scaling").