Quantum metrology with non-equilibrium steady states of quantum spin chains

Abstract

We consider parameter estimations with probes being the boundary driven/dissipated non- equilibrium steady states of XXZ spin 1/2 chains. The parameters to be estimated are the dissipation coupling and the anisotropy of the spin-spin interaction. In the weak coupling regime we compute the scaling of the Fisher information, i.e. the inverse best sensitivity among all estimators, with the number of spins. We find superlinear scalings and transitions between the distinct, isotropic and anisotropic, phases. We also look at the best relative error which decreases with the number of particles faster than the shot-noise only for the estimation of anisotropy.

12 pages, 10 figures

References in corpus (20)

• Nonlinear atom interferometer surpasses classical precision limit
• Entanglement-free Heisenberg-limited phase estimation
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Generalized Limits for Single-Parameter Quantum Estimation
• Modeling heat transport through completely positive maps
• Phase estimation without a priori knowledge in the presence of loss
• Quasilocal conservation laws in XXZ spin-1/2 chains: open, periodic and twisted boundary conditions
• Quantum-limited metrology with product states
• Radio-frequency magnetometry using a single electron spin
• Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
• Hamiltonian tomography in an access-limited setting without state initialization
• Entanglement in fermion systems and quantum metrology
• Indirect Hamiltonian Identification through a small gateway
• Nano-Kelvin thermometry and temperature control: beyond the thermal noise limit
• Indirect Quantum Tomography of Quadratic Hamiltonians
• Squeezing Inequalities and Entanglement for Identical Particles
• Collectively enhanced quantum measurements at the Heisenberg limit
• A tomographic approach to non-Markovian master equations
• Quantum Seismology
• Probing a composite spin-boson environment

Cited by in corpus (27)

• Quantum enhanced measurements without entanglement
• Geometry of quantum phase transitions
• Genuine quantum correlations in quantum many-body systems: a review of recent progress
• On quantumness in multi-parameter quantum estimation
• Geometry and response of Lindbladians
• At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
• Universal time scaling for Hamiltonian parameter estimation
• Dynamical Quantum Phase Transitions: A Geometric Picture
• Probing the anomalous dynamical phase in long-range quantum spin chains through Fisher-zero lines
• Floquet dynamical phase transition and entanglement spectrum
• Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• Quantum metrology for the Ising Hamiltonian with transverse magnetic field
• Quantum Fisher information and symmetric logarithmic derivative via anti-commutators
• Information geometric methods for complexity
• Non-equilibrium magnetic phases in spin lattices with gain and loss
• Coherence enhanced quantum metrology in a nonequilibrium optical molecule
• Quantum metrology of spatial deformation using arrays of classical and quantum light emitters
• Quantum metrology in local dissipative environments
• Determining the Continuous Family of Quantum Fisher Information from Linear Response Theory
• Estimation of pulsed driven qubit parameters via quantum Fisher information
• Driven quantum spin chain in the presence of noise: Anti-Kibble-Zurek behavior
• Fluctuation-dissipation theorem for non-equilibrium quantum systems
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Quantum metrology out of equilibrium
• Quantum uncertainty in critical systems with three spins interaction
• Computational complexity of non-equilibrium steady states of quantum spin chains