Precision bounds for multiple currents in open quantum systems

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.

Updated version with new Figs. 2 and 3 and fixed typos

References in corpus (40)

• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Thermodynamic uncertainty relation for biomolecular processes
• Dissipation bounds all steady-state current fluctuations
• Irreversible entropy production, from quantum to classical
• Fundamental Quantum Limit to Waveform Estimation
• Condition for macroscopic realism beyond the Leggett-Garg inequalities
• Thermodynamics of precision in quantum non equilibrium steady states
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• On the validity of the thermodynamic uncertainty relation in quantum systems
• The Fisher information and the quantum Cramer-Rao sensitivity limit of continuous measurements
• Multidimensional thermodynamic uncertainty relations
• A strict experimental test of macroscopic realism in a superconducting flux qubit
• Quantum thermodynamic uncertainty relation for continuous measurement
• Uncertainty relations in stochastic processes: An information inequality approach
• Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
• Entropy production along nonequilibrium quantum jump trajectories
• Kinetic uncertainty relation
• Frenesy: time-symmetric dynamical activity in nonequilibria
• Bayesian parameter inference from continuously monitored quantum systems
• Coherence-enhanced constancy of a quantum thermoelectric generator
• Thermodynamic uncertainty relation in quantum thermoelectric junctions
• Violating the Thermodynamic Uncertainty Relation in the Three-Level Maser
• Restoring Heisenberg scaling in noisy quantum metrology by monitoring the environment
• Thermodynamics of Precision in Markovian Open Quantum Dynamics
• Signatures of quantum behavior in single-qubit weak measurements
• Frenetic bounds on the entropy production
• Uncertainty relations for underdamped Langevin dynamics
• Thermodynamics of precision in quantum nano-machines
• Entanglement and thermokinetic uncertainty relations in coherent mesoscopic transport
• Nonclassical time correlation functions in continuous quantum measurement
• Thermodynamic uncertainty relation for first-passage times on Markov chains
• Kinetic uncertainty relation on first passage time for accumulated current
• Quantum Martingale Theory and Entropy Production
• Parameter estimation and system identification for continuously-observed quantum systems
• Role of Quantum Coherence in Kinetic Uncertainty Relations
• Modeling Leggett-Garg-inequality violation
• Quantifying quantum invasiveness
• Probing quantumness with joint continuous measurements of non-commuting qubit observables
• Time-resolved Stochastic Dynamics of Quantum Thermal Machines
• Connecting measurement invasiveness to optimal metrological scenarios

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• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Quasiprobability Thermodynamic Uncertainty Relation
• Tightening the thermodynamic uncertainty relations with null-entropy events: What we learn when nothing happens
• Response kinetic uncertainty relation for Markovian open quantum systems
• Current fluctuations in nonequilibrium open quantum systems beyond weak coupling: a reaction coordinate approach
• Universal Precision Limits in General Open Quantum Systems
• Information-thermodynamic bounds on precision in interacting quantum systems