Formulation of Time-Resolved Counting Statistics Based on a Positive-Operator-Valued Measure

TL;DR

This paper introduces a new method for deriving full counting statistics of electronic current using positive-operator-valued measures, justifying existing formulas and extending to finite-frequency noise, with experimental implications.

Contribution

It presents a novel derivation framework for counting statistics that generalizes the Levitov-Lesovik formula to finite frequencies and predicts additional white noise effects.

Findings

Justifies the Levitov-Lesovik formula in the long-time limit

Predicts an additional white noise at high frequencies

Proposes an experimental test for high- and low-frequency noise measurement

Abstract

We propose a derivation of the full counting statistics of electronic current based on a positive-operator-valued measure. Our approach justifies the Levitov-Lesovik formula in the long-time limit, but can be generalized to the detection of finite-frequency noise correlations. The combined action of the projection postulate and the quantum formula for current noise at high frequencies imply an additional white noise. Estimates for this additional noise are in accordance with known experiments. We propose an experimental test of our conjecture by a simultaneous measurement of high- and low-frequency noise.