Yoshiyuki Tsuda and Keiji Matsumoto 2005 J. Phys. A: Math. Gen. 38 1593 doi:10.1088/0305-4470/38/7/014
Yoshiyuki Tsuda1 and Keiji Matsumoto2,3
Show affiliationsState estimation is a classical problem in quantum information. In optimization of an estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use a derivative of the density matrix. However, sometimes, we are interested in quantities with singularity, e.g. concurrence etc. In this paper, lower bounds to a mean square error of an estimator are derived for a quantum estimation problem without smoothness assumptions. Our main idea is to replace the derivative by difference, as is done in classical estimation theory. We applied the inequalities to several examples, and derived an optimal estimator for some of them.
Issue 7 (18 February 2005)
Received 19 October 2004, in final form 15 December 2004
Published 2 February 2005
Yoshiyuki Tsuda and Keiji Matsumoto 2005 J. Phys. A: Math. Gen. 38 1593
Stephen W Hughes 2006 Phys. Educ. 41 144
N W Marshall et al 2001 Phys. Med. Biol. 46 1283
Akio Kotani et al 2009 J. Phys.: Conf. Ser. 190 012013
Yong-Kwan Kim et al 2006 Nanotechnology 17 1375
Marek A Abramowicz et al 2006 Class. Quantum Grav. 23 1689
J Purans et al 2009 J. Phys.: Conf. Ser. 190 012063
S B Lobb et al 2009 J. Phys. A: Math. Theor. 42 472002
Ma Zhen-He et al 2006 Chinese Phys. Lett. 23 366
M. Aichhorn and E. Arrigoni 2005 Europhys. Lett. 72 117