Recently, violation of Heisenberg’s uncertainty relation in spin
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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 σx and σy, 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 ±1 as measurement outcome. This conclusion agrees with recent researches
[K. Nagata, Int. J. Theor. Phys. 48, 3532 (2009)] and [K. Nagata et al.,
Int. J. Theor. Phys. 49, 162 (2010)].
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