New bounds on adaptive quantum metrology under Markovian noise

Abstract

We analyse the problem of estimating a scalar parameter $g$ that controls the Hamiltonian of a quantum system subject to Markovian noise. Specifically, we place bounds on the growth rate of the quantum Fisher information with respect to $g$, in terms of the Lindblad operators and the $g$-derivative of the Hamiltonian $H$. Our new bounds are not only more generally applicable than those in the literature -- for example, they apply to systems with time-dependent Hamiltonians and/or Lindblad operators, and to infinite-dimensional systems such as oscillators -- but are also tighter in the settings where previous bounds do apply. We derive our bounds directly from the stochastic master equation describing the system, without needing to discretise its time evolution. We also use our results to investigate how sensitive a single detection system can be to signals with different time dependences. We demonstrate that the sensitivity bandwidth is related to the quantum fluctuations of $\partial H/\partial g$, illustrating how 'non-classical' states can enhance the range of signals that a system is sensitive to, even when they cannot increase its peak sensitivity.

arXiv comment21 pages, 2 figures; journal version

References in corpus (34)

• Advances in Quantum Metrology
• Dynamical Decoupling of Open Quantum Systems
• Dynamical suppression of decoherence in two-state quantum systems
• Quantum metrology from a quantum information science perspective
• Experimental Searches for the Axion and Axion-like Particles
• Quantum Fisher Information Flow in Non-Markovian Processes of Open Systems
• Macroscopically distinct quantum superposition states as a bosonic code for amplitude damping
• Using entanglement against noise in quantum metrology
• Achieving the Heisenberg limit in quantum metrology using quantum error correction
• Fundamental Quantum Limit to Waveform Estimation
• Multi-parameter estimation beyond Quantum Fisher Information
• Searching for Dark Matter with a Superconducting Qubit
• Optimal quantum-enhanced interferometry using a laser power source
• Gravitational Waves from Neutron Stars: A Review
• Efficient tools for quantum metrology with uncorrelated noise
• Adaptive quantum metrology under general Markovian noise
• Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
• Discontinuities of the quantum Fisher information and the Bures metric
• Quantum metrology with full and fast quantum control
• Bounds on the Lambert function and their application to the outage analysis of user cooperation
• Ultimate Precision of Adaptive Noise Estimation
• Squeezed vacuum used to accelerate the search for a weak classical signal
• Asymptotic theory of quantum channel estimation
• Optimal probes and error-correction schemes in multi-parameter quantum metrology
• Asymptotic role of entanglement in quantum metrology
• Towards the Fundamental Quantum Limit of Linear Measurements of Classical Signals
• Optimal approximate quantum error correction for quantum metrology
• Ancilla-Assisted Enhancement of Channel Estimation for Low-Noise Parameters
• Energetic Quantum Limit in Large-Scale Interferometers
• Continuity of the quantum Fisher information
• Parametrics of electromagnetic searches for axion dark matter
• Optimal estimation and discrimination of excess noise in thermal and amplifier channels
• N-body-extended Channel Estimation for Low-Noise Parameters
• Fundamental Relations between Measurement, Radiation and Decoherence in Gravitational Wave Laser Interferometer Detectors

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• The advantage of quantum control in many-body Hamiltonian learning
• Limits of noisy quantum metrology with restricted quantum controls
• Interplay between time and energy in bosonic noisy quantum metrology
• Achieving metrological limits using ancilla-free quantum error-correcting codes
• A tensor network approach to sensing quantum light-matter interactions
• Universal time scalings of sensitivity in Markovian quantum metrology
• Lindblad estimation with fast and precise quantum control
• Time correlations from steady-state expectation values
• Parameter estimation with one- and two-time measurements on the emission field of the boundary time crystal