%0 Journal Article
%T Violation of Heisenberg¡¯s Uncertainty Principle
%A Koji Nagata
%A Tadao Nakamura
%J Open Access Library Journal
%V 2
%N 8
%P 1-6
%@ 2333-9721
%D 2015
%I Open Access Library
%R 10.4236/oalib.1101797
%X Recently, violation of Heisenberg¡¯s uncertainty relation in spin
measurements is discussed [J. Erhart<i> et al.</i>, Nature Physics 8, 185
(2012)] and [G. Sulyok <i>et al.</i>, Phys. Rev. A 88, 022110 (2013)]. We
derive the optimal limitation of Heisenberg¡¯s uncertainty principle in a
specific two-level system (e.g., electron spin, photon polarizations, and so
on). Some physical situation is that we would measure <strong>¦Ò</strong><sub><strong>x</strong></sub> and <span style="white-space:normal;"><strong>¦Ò</strong></span><sub style="white-space:normal;"><strong>y</strong></sub>, simultaneously. The
optimality is certified by the Bloch sphere. We show that a violation of
Heisenberg¡¯s uncertainty principle means a violation of the Bloch sphere in the
specific case. Thus, the above experiments show a violation of the Bloch sphere
when we use ¡À1 as measurement outcome. This conclusion agrees with recent researches
[K. Nagata, Int. J. Theor. Phys. 48, 3532 (2009)] and [K. Nagata<i> et al.</i>,
Int. J. Theor. Phys. 49, 162 (2010)].
%K Quantum Measurement Theory
%K Quantum Information Theory
%U http://www.oalib.com/paper/3149126