Open Access
May 2011 An approximate quantum Cramér–Rao bound based on skew information
Alessandra Luati
Bernoulli 17(2): 628-642 (May 2011). DOI: 10.3150/10-BEJ285


A closed-form expression for Wigner–Yanase skew information in mixed-state quantum systems is derived. It is shown that limit values of the mixing coefficients exist such that Wigner–Yanase information is equal to Helstrom information. The latter constitutes an upper bound for the classical expected Fisher information, hence the inverse Wigner–Yanase information provides an approximate lower bound to the variance of an unbiased estimator of the parameter of interest. The advantage of approximating Helstrom’s sharp bound lies in the fact that Wigner–Yanase information is straightforward to compute, while it is often very difficult to obtain a feasible expression for Helstrom information. In fact, the latter requires the solution of an implicit second order matrix differential equation, while the former requires just scalar differentiation.


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Alessandra Luati. "An approximate quantum Cramér–Rao bound based on skew information." Bernoulli 17 (2) 628 - 642, May 2011.


Published: May 2011
First available in Project Euclid: 5 April 2011

zbMATH: 1345.62044
MathSciNet: MR2787608
Digital Object Identifier: 10.3150/10-BEJ285

Keywords: Cramér–Rao-type bounds , Fisher information , Parametric quantum models

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

Vol.17 • No. 2 • May 2011
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