Precision bounds for multiple currents in open quantum systems

TL;DR

This paper derives tighter multidimensional quantum uncertainty relations for multiple currents in open quantum systems, revealing quantum correlations and surpassing classical bounds by leveraging Fisher information matrix analysis.

Contribution

It introduces multidimensional quantum TUR and KUR for multiple observables, incorporating correlations via Fisher information, and demonstrates their tightness and quantum signatures.

Findings

Bounds are tighter than previous single-observable quantum TURs and KURs.

Quantum correlations are captured by off-diagonal Fisher information matrix elements.

Multidimensional bounds can be saturated with perfectly correlated observables.

Abstract

Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these classical bounds in open quantum systems, motivating the derivation of new quantum TURs and KURs that account for the role of quantum coherence. Here, we go one step further by deriving multidimensional KUR and TUR for multiple observables in open quantum systems undergoing Markovian dynamics. Our derivation exploits a multi-parameter metrology approach, in which the Fisher information matrix plays a central role. Crucially, our bounds are tighter than previously derived quantum TURs and KURs for single observables, precisely because they incorporate correlations between multiple observables. We also find an intriguing quantum signature of correlations that is captured by the off-diagonal element of the Fisher information matrix, which vanishes for classical stochastic dynamics. By considering two examples, namely a coherently driven qubit system and the three-level maser, we demonstrate that the multidimensional quantum KUR bound can even be saturated when the observables are perfectly correlated.