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.

arXiv comment8 pages, 4 figures, improved presentation, to appear in PRA

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• Equivalence classes and local asymptotic normality in system identification for quantum Markov chains
• Parameter estimation and system identification for continuously-observed quantum systems
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• Improving quantum parameter estimation by monitoring quantum trajectories
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