An upper bound on the number of compatible parameters in simultaneous quantum estimation

Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not necessarily achievable. There exists a necessary and sufficient con...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-03, Vol.53 (9), p.95303
Main Author: Kukita, Shingo
Format: Article
Language:English
Subjects:
quantum Fisher information
quantum information
simultaneous estimation
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Summary:Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not necessarily achievable. There exists a necessary and sufficient condition for its achievability. It is unknown how many parameters can be estimated while satisfying this condition. In this paper, we analyse an upper bound on the number of such parameters through linear-algebraic techniques. This upper bound depends on the algebraic structure of the quantum system used as a probe. We explicitly calculate this bound for two quantum systems: single qubit and two-qubit X-states.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/ab6d3d