Exceptional points for parameter estimation in open quantum systems: Analysis of the Bloch equations

Abstract

We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: The dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator ${\cal L}$. The eigenvalues of ${\cal L}$ are complex, reflecting unitary as well as dissipative dynamics. For certain values of parameters defining ${\cal L}$, non-hermitian degeneracies emerge, i.e. exceptional points ($EP$). The dynamical signature of these $EP$s corresponds to a unique time evolution. This unique feature can be employed experimentally to locate the $EP$s and thereby to determine the intrinsic system parameters with a high accuracy. This way we turn the disadvantage of the dissipation into an advantage. We demonstrate this method in the open system dynamics of a two-level system described by the Bloch equation, which has become the paradigm of diverse fields in physics, from NMR to quantum information and elementary particles.