Role of Quantum Coherence in Kinetic Uncertainty Relations

TL;DR

This paper investigates how quantum coherence influences the violation of classical kinetic uncertainty relations, deriving a modified bound that clarifies the role of coherence in quantum stochastic processes.

Contribution

The authors derive a new bound that precisely relates quantum coherence to violations of the classical Kinetic Uncertainty Relation, considering different quantum unravelings.

Findings

Quantum coherence can lead to violations of the classical KUR.

The modified bound depends on the type of quantum measurement unraveling.

Application to a double quantum dot illustrates the theoretical results.

Abstract

The Kinetic Uncertainty Relation (KUR) bounds the signal-to-noise ratio of stochastic currents in terms of the number of transitions per unit time, known as the dynamical activity. This bound was derived in a classical context, and can be violated in the quantum regime due to coherent effects. However, the precise connection between KUR violations and quantum coherence has so far remained elusive, despite significant investigation. In this work, we solve this problem by deriving a modified bound that exactly pinpoints how, and when, coherence might lead to KUR violations. Our bound is sensitive to the specific kind of unraveling of the quantum master equation. It therefore allows one to compare quantum jumps and quantum diffusion, and understand, in each case, how quantum coherence affects fluctuations. We illustrate our result on a double quantum dot, where the electron current is monitored either by electron jump detection or with continuous diffusive charge measurement.