An approximate quantum Cramér--Rao bound based on skew information

Details An approximate quantum Cramér--Rao bound based on skew information An approximate quantum Cramér--Rao bound based on skew information

2011-04-21

arxiv.org/abs/1104.4252v1

Bernoulli 2011, Vol. 17, No. 2, 628-642

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ285 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

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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