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Robertson, H.P. (1929) The Uncertainty Principle. Physical Review, 34, 163-164.

has been cited by the following article:

  • TITLE: Violation of Heisenberg’s Uncertainty Principle

    AUTHORS: Koji Nagata, Tadao Nakamura

    KEYWORDS: Quantum Measurement Theory, Quantum Information Theory

    JOURNAL NAME: Open Access Library Journal, Vol.2 No.8, August 12, 2015

    ABSTRACT: Recently, violation of Heisenberg’s uncertainty relation in spin measurements is discussed [J. Erhart et al., Nature Physics 8, 185 (2012)] and [G. Sulyok et al., 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 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)].