Current-based metrology with two-terminal mesoscopic conductors

TL;DR

This paper develops a current-based quantum metrology framework for two-terminal mesoscopic conductors, providing analytical bounds on estimation precision across various regimes and identifying the optimal transmission function.

Contribution

It introduces a novel approach to quantum metrology based on currents in mesoscopic conductors, extending analysis beyond Markovian assumptions and identifying optimal transmission functions.

Findings

Analytical precision bounds in linear-response and zero-temperature regimes.

Boxcar transmission function is optimal for current-based metrology.

Framework applicable to arbitrary coupling and temperature regimes.

Abstract

The traditional approach to quantum parameter estimation focuses on the quantum state, deriving fundamental bounds on precision through the quantum Fisher information. In most experimental settings, however, performing arbitrary quantum measurements is highly unfeasible. In open quantum systems, an alternative approach to metrology involves the measurement of stochastic currents flowing from the system to its environment. However, the present understanding of current-based metrology is mostly limited to Markovian master equations. Considering a parameter estimation problem in a two-terminal mesoscopic conductor, we identify the key elements that determine estimation precision within the Landauer-B\"uttiker formalism. Crucially, this approach allows us to address arbitrary coupling and temperature regimes. Furthermore, we obtain analytical results for the precision in linear-response and zero-temperature regimes. For the specific parameter estimation task that we consider, we demonstrate that the boxcar transmission function is optimal for current-based metrology in all parameter regimes.