Channel Estimation Theory of Low-Noise Multiple Parameters:Attainablity Problem of the Cram{é}r-Rao Bounds

For decoherence processes induced by weak interactions with the environment, a general quantum channel with one noise parameter has been formulated. This channel is called low-noise channel and very useful for investigating the parameter estimation in the leading order. In this paper, we formulate t...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2008-03
Main Authors: Hotta, Masahiro, Karasawa, Tokishiro
Format: Article
Language:English
Subjects:
Commutativity
Entanglement
Noise
Order parameters
Parameter estimation
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:For decoherence processes induced by weak interactions with the environment, a general quantum channel with one noise parameter has been formulated. This channel is called low-noise channel and very useful for investigating the parameter estimation in the leading order. In this paper, we formulate the low-noise channel with multiple unknown parameters in order to address the simultaneous achievability of the Cram{é}r-Rao bound for the parameters estimation. In general, the simultaneous achievement of the Cram{é}r-Rao bound for multi-parameter estimations suffers from non-commutativity of optimal measurements for respective parameters. However, with certain exceptions, we show that the Cram{é}r-Rao bound for output states of dissipative low-noise channels can be always attained in the first order of the parameters as long as D \leq N-1, where D and N denote the number of the parameters and the dimension of the system, respectively. This condition is replaced by D \leq N^{2}-1 if it is allowed to set the entanglement with ancilla systems in its input state and to perform the non-local measurement on the composite system.
ISSN:2331-8422
DOI:10.48550/arxiv.0803.0613