N-body-extended Channel Estimation for Low-Noise Parameters

Abstract

The notion of low-noise channels was recently proposed and analyzed in detail in order to describe noise-processes driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005)]. An estimation theory of low-noise parameters of channels has also been developed. In this report, we address the low-noise parameter estimation problem for the $N$-body extension of low-noise channels. We perturbatively calculate the Fisher information of the output states in order to evaluate the lower-bound of the mean-square error of the parameter estimation. We show that the maximum of the Fisher information over all input states can be attained by a factorized input state in the leading order of the low-noise parameter. Thus, to achieve optimal estimation, it is not necessary for there to be entanglement of the $N$ subsystems, as long as the true low-noise parameter is sufficiently small.

10 pages, 1 figure

References in corpus (7)

• Optimal discrimination of quantum operations
• Optimal estimation of group transformations using entanglement
• Estimation of unitary quantum operations
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• Minimax discrimination of two Pauli channels
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• Squeezed vacuum as a universal quantum probe
• Asymptotic theory of quantum channel estimation
• New bounds on adaptive quantum metrology under Markovian noise
• Channel Estimation Theory of Low-Noise Multiple Parameters:Attainablity Problem of the Cram{é}r-Rao Bounds
• Parameter estimation by decoherence in the double-slit experiment