Violation of Heisenberg’s Uncertainty Principle

DOI: 10.4236/oalib.1101797   PDF   HTML   XML   1,003 Downloads   2,538 Views   Citations


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)].

Share and Cite:

Nagata, K. and Nakamura, T. (2015) Violation of Heisenberg’s Uncertainty Principle. Open Access Library Journal, 2, 1-6. doi: 10.4236/oalib.1101797.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Sakurai, J.J. (1995) Modern Quantum Mechanics. Addison-Wesley Publishing Company.
[2] Peres, A. (1993) Quantum Theory: Concepts and Methods. Kluwer Academic, Dordrecht.
[3] Redhead, M. (1989) Incompleteness, Nonlocality, and Realism. 2nd Edition, Clarendon Press, Oxford.
[4] von Neumann, J. (1955) Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton.
[5] Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge.
[6] Leggett, A.J. (2003) Nonlocal Hidden-Variable Theories and Quantum Mechanics: An Incompatibility Theorem. Foundations of Physics, 33, 1469-1493.
[7] Gröblacher, S., Paterek, T., Kaltenbaek, R., Brukner, Č., Żukowski, M., Aspelmeyer, M. and Zeilinger, A. (2007) An Experimental Test of Non-Local Realism. Nature (London), 446, 871-875.
[8] Paterek, T., Fedrizzi, A., Gröblacher, S., Jennewein, T., Żukowski, M., Aspelmeyer, M. and Zeilinger, A. (2007) Experimental Test of Nonlocal Realistic Theories without the Rotational Symmetry Assumption. Physical Review Letters, 99, Article ID: 210406.
[9] Branciard, C., Ling, A., Gisin, N., Kurtsiefer, C., Lamas-Linares, A. and Scarani, V. (2007) Experimental Falsification of Leggett’s Nonlocal Variable Model. Physical Review Letters, 99, Article ID: 210407.
[10] Deutsch, D. (1985) Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer. Proceedings of the Royal Society of London. Series A, 400, 97.
[11] Jones, J.A. and Mosca, M. (1998) Implementation of a Quantum Algorithm on a Nuclear Magnetic Resonance Quantum Computer. The Journal of Chemical Physics, 109, 1648.
[12] Gulde, S., Riebe, M., Lancaster, G.P.T., Becher, C., Eschner, J., Häffner, H., Schmidt-Kaler, F., Chuang, I.L. and Blatt, R. (2003) Implementation of the Deutsch-Jozsa Algorithm on an Ion-Trap Quantum Computer. Nature, 421, 48-50.
[13] de Oliveira, A.N., Walborn, S.P. and Monken, C.H. (2005) Implementing the Deutsch Algorithm with Polarization and Transverse Spatial Modes. Journal of Optics B: Quantum and Semiclassical Optics, 7, 288-292.
[14] Kim, Y.-H. (2003) Single-Photon Two-Qubit Entangled States: Preparation and Measurement. Physical Review A, 67, Article ID: 040301(R).
[15] Mohseni, M., Lundeen, J.S., Resch, K.J. and Steinberg, A.M. (2003) Experimental Application of Decoherence-Free Subspaces in an Optical Quantum-Computing Algorithm. Physical Review Letters, 91, Article ID: 187903.
[16] Tame, M.S., Prevedel, R., Paternostro, M., Böhi, P., Kim, M.S. and Zeilinger, A. (2007) Experimental Realization of Deutsch’s Algorithm in a One-Way Quantum Computer. Physical Review Letters, 98, Article ID: 140501.
[17] Heisenberg, W. (1927) über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43, 172-198.
[18] Kennard, E.H. (1927) Zur Quantenmechanik einfacher Bewegungstypen. Zeitschrift für Physik, 44, 326-352.
[19] Weyl, H. (1928) Gruppentheorie und Quantenmechanik. Hirzel, Leipzig.
[20] Ozawa, M. (2003) Universally Valid Reformulation of the Heisenberg Uncertainty Principle on Noise and Disturbance in Measurement. Physical Review A, 67, Article ID: 042105.
[21] Erhart, J., Sponar, S., Sulyok, G., Badurek, G., Ozawa, M. and Hasegawa, Y. (2012) Experimental Demonstration of a Universally Valid Error-Disturbance Uncertainty Relation in Spin Measurements. Nature Physics, 8, 185-189.
[22] Sulyok, G., Sponar, S., Erhart, J., Badurek, G., Ozawa, M. and Hasegawa, Y. (2013) Violation of Heisenberg’s Error-Disturbance Uncertainty Relation in Neutron-Spin Measurements. Physical Review A, 88, Article ID: 022110.
[23] Nagata, K. (2009) There Is No Axiomatic System for the Quantum Theory. International Journal of Theoretical Physics, 48, 3532-3536.
[24] Nagata, K. and Nakamura, T. (2010) Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm? International Journal of Theoretical Physics, 49, 162-170.
[25] Robertson, H.P. (1929) The Uncertainty Principle. Physical Review, 34, 163-164.
[26] Schrödinger, E. (1930) Zum Heisenbergschen Unscharfeprinzip. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 14, 296-303.
[27] Griffiths, D. (2005) Quantum Mechanics. Pearson Prentice Hall, Upper Saddle River.
[28] Riley, K.F., Hobson, M.P. and Bence, S.J. (2006) Mathematical Methods for Physics and Engineering. Cambridge University Press, Cambridge, 246.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.