Role of topology in determining the precision of a finite thermometer

Abstract

Temperature fluctuations of a finite system follows the Landau bound $\delta T^2=T^2/C(T)$ where $C(T)$ is the heat capacity of the system. In turn, the same bound sets a limit to the precision of temperature estimation when the system itself is used as a thermometer. In this paper, we employ graph theory and the concept of Fisher information to assess the role of topology on the thermometric performance of a given system. We find that low connectivity is a resource to build precise thermometers working at low temperatures, whereas highly connected systems are suitable for higher temperatures. Upon modelling the thermometer as a set of vertices for the quantum walk of an excitation, we compare the precision achievable by position measurement to the optimal one, which itself corresponds to energy measurement.

arXiv comment16 pages, 8 figures, accepted version

References in corpus (42)

• A nonequilibrium equality for free energy differences
• Quantifying Coherence
• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications
• Quantum Fisher information matrix and multiparameter estimation
• The second laws of quantum thermodynamics
• Resolved Sideband Cooling of a Micromechanical Oscillator
• Preparation and Detection of a Mechanical Resonator Near the Ground State of Motion
• Individual quantum probes for optimal thermometry
• Entanglement in Quantum Information Theory
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Irreversible work and inner friction in quantum thermodynamic processes
• Quantum Limits of Thermometry
• Single-qubit thermometry
• Bures metric over thermal state manifolds and quantum criticality
• Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers
• In situ thermometry of a cold Fermi gas via dephasing impurities
• Quantum thermodynamics of general quantum processes
• Local quantum thermal susceptibility
• Qubit thermometry for micromechanical resonators
• Robust quantum optimizer with full connectivity
• Qubit-assisted thermometry of a quantum harmonic oscillator
• Quantum measurement and the first law of thermodynamics: the energy cost of measurement is the work value of the acquired information
• Quantum limits of cold damping with optomechanical coupling
• Quantum thermometry by single-qubit dephasing
• Fundamental limits on low-temperature quantum thermometry with finite resolution
• Precision Measurements of Temperature and Chemical Potential of Quantum Gases
• Achieving the Landau bound to precision of quantum thermometry in systems with vanishing gap
• Estimating Temperature via Sequential Measurements
• Enhanced precision bound of low-temperature quantum thermometry via dynamical control
• Thermometry Precision in Strongly Correlated Ultracold Lattice Gases
• Laplacian versus Adjacency Matrix in Quantum Walk Search
• Probing BEC phase fluctuations with atomic quantum dots
• Out-of-equilibrium Thermodynamics of Quantum Optomechanical Systems
• Tight bound on finite-resolution quantum thermometry at low temperatures
• Quantum thermometry using the ac Stark shift within the Rabi model
• On quantum interferometric measurements of temperature
• Fluctuation relations for driven coupled classical two-level systems
• Geometry of quantum observables and thermodynamics of small systems
• Continuous-time quantum walks on planar lattices and the role of the magnetic field
• Quantum metrology out of equilibrium
• Sharpening the Second Law of Thermodynamics with the Quantum Bayes' Theorem

Cited by in corpus (4)

• Enhancing precision thermometry with nonlinear qubits
• Effects of counter-rotating-wave terms on the noisy frequency estimation
• Optimizing quantum sensing networks via genetic algorithms and deep learning
• Configuration-dependent precision in magnetometry and thermometry using multi-qubit quantum sensors