Uncertainty relations from Fisher information

J. S. Dehesa, Rodolfo O. Esquivel, Angel Ricardo Plastino +1 more

Shunlong Luo

Cecilia N. Isonguyo, K. J. Oyewumi, Opeyemi S. Oyun +1 more

The Heisenberg uncertainty relation as well as the Fisher information are presented analytically and numerically for the Generalized radial Yukawa potential. The probability density for the ground and first excited state has been analyzed via the Fisher information for this potential model. Some numerical results are obtained. From the numerical results obtained, we observed that, for n = 0, 1, the position-space Fisher information Ir increases with increasing potential parameter a, while the momentum-space Fisher information Iρ initially increases, and later decreases with increasing potential parameter a. The Fisher-information-based uncertainty relation and the Heisenberg uncertainty relation have been verified to hold for this atomic model. In addition, we observed a squeezed phenomenon in some of the results in position r and momentum ρ for the ground and first excited states.

B. Roy Frieden

Kenjiro Yanagi, Shigeru Furuichi, Ken Kuriyama

We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S.Luo for the quantum uncertainty quantity excluding the classical mixture. And we introduce a generalized Fisher information and then derive a generalized Cramer-Rao inequality. We also give an example for our generalized Fisher information and then derive the uncertainty relation for two observables.

Paolo Gibilisco, Tommaso Isola