An approximate quantum Cramér–Rao bound based on skew information
Luati, Alessandra
Bernoulli, Tome 17 (2011) no. 1, p. 628-642 / Harvested from Project Euclid
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.
Publié le : 2011-05-15
Classification:  Cramér–Rao-type bounds,  Fisher information,  parametric quantum models
@article{1302009240,
     author = {Luati, Alessandra},
     title = {An approximate quantum Cram\'er--Rao bound based on skew information},
     journal = {Bernoulli},
     volume = {17},
     number = {1},
     year = {2011},
     pages = { 628-642},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1302009240}
}
Luati, Alessandra. An approximate quantum Cramér–Rao bound based on skew information. Bernoulli, Tome 17 (2011) no. 1, pp.  628-642. http://gdmltest.u-ga.fr/item/1302009240/