Heisenberg versus standard scaling in quantum metrology with Markov generated states and monitored environment

Abstract

Finding optimal and noise robust probe states is a key problem in quantum metrology. In this paper we propose Markov dynamics as a possible mechanism for generating such states, and show how the Heisenberg scaling emerges for systems with multiple `dynamical phases' (stationary states), and noiseless channels. We model noisy channels by coupling the Markov output to `environment' ancillas, and consider the scenario where the environment is monitored to increase the quantum Fisher information of the output. In this setup we find that the survival of the Heisenberg limit depends on whether the environment receives `which phase' information about the memory system.

8 pages, 4 figures, improved presentation, to appear in PRA

References in corpus (4)

• The density-matrix renormalization group in the age of matrix product states
• Optimal Quantum Phase Estimation
• Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state
• Fisher information and asymptotic normality in system identification for quantum Markov chains

Cited by in corpus (4)

• Ultimate limits for quantum magnetometry via time-continuous measurements
• Parameter estimation and system identification for continuously-observed quantum systems
• Probe thermometry with continuous measurements
• Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels