Measuring a Quantum System’s Classical Information

ABSTRACT

In the governing thought, I find an equivalence between the classical information in a quantum system and the integral of that system’s energy and time, specifically , in natural units. I solve this relationship in four ways: the first approach starts with the Schrodinger Equation and applies the Minkowski transformation; the second uses the Canonical commutation relation; the third through Gabor’s analysis of the time-frequency plane and Heisenberg’s uncertainty principle; and lastly by quantizing Brownian motion within the Bernoulli process and applying the Gaussian channel capacity. In support I give two examples of quantum systems that follow the governing thought: namely the Gaussian wave packet and the electron spin. I conclude with comments on the discretization of space and the information content of a degree of freedom.

Cite this paper

J. Haller Jr., "Measuring a Quantum System’s Classical Information,"*Journal of Modern Physics*, Vol. 5 No. 1, 2014, pp. 8-16. doi: 10.4236/jmp.2014.51002.

J. Haller Jr., "Measuring a Quantum System’s Classical Information,"

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[1] J. Gantz and D. Reinsel, “The Digital Universe in 2020,” IDC, Framingham, 2012.

[2] J. Manyika, et al., “Big Data: The Next Frontier for Innovation, Competition, and Productivity,” McKinsey Global Institute, San Francisco, 2011.

[3] L. Brillouin, “Science and Information Theory,” 2nd Edition, Academic Press Inc., Waltham, 1962.

[4] B. Schumacher and M. Westmoreland, “Quantum Processes, Systems, and Information,” Cambridge University Press, Cambridge, 2010.

[5] L. Smolin, “The Trouble With Physics,” First Mariner Books, New York, 2006

[6] C. Shannon and W. Weaver, “The Mathematical Theory of Communication,” University of Illinois Press, Champaign, 1949.

[7] M. Volkenstein, “Entropy and Information,” Birkhauser, Berlin, 2009.

http://dx.doi.org/10.1007/978-3-0346-0078-1

[8] F. Reif, “Fundamentals of Statistical and Thermal Physics,” McGraw Hill, Boston, 1965.

[9] T. Cover and J. Thomas, “Elements of Information Theory,” John Wiley & Sons Inc., New York, 1991.

http://dx.doi.org/10.1002/0471200611

[10] R. Feynman, “Lectures on Physics,” Addison-Wesley Publishing, Reading, 1965.

[11] A. Einstein, “The Meaning of Relativity,” Princeton University Press, Princeton, 1953.

[12] R. Shankar, “Principles of Quantum Mechanics,” 2nd Edition, Plenum Press, New York, 1994.

http://dx.doi.org/10.1007/978-1-4757-0576-8

[13] H. Nyquist, Bell System Technical Journal, Vol. 3, 1924, pp. 324-326.

http://dx.doi.org/10.1002/j.1538-7305.1924.tb01361.x

[14] R. V. L. Hartley, Bell System Technical Journal, Vol. 7, 1928, pp. 535-563.

http://dx.doi.org/10.1002/j.1538-7305.1928.tb01236.x

[15] D. Gabor, Journal of Institution of Electrical Engineers, Vol. 93, 1946, p. 429.

[16] D. Slepian and H. O. Pollak, Bell System Technical Journal, Vol. 40, 1961, pp. 43-63.

http://dx.doi.org/10.1002/j.1538-7305.1961.tb03976.x

[17] H. J. Landau and H. O. Pollak, Bell System Technical Journal, Vol. 40, 1961, pp. 65-84.

http://dx.doi.org/10.1002/j.1538-7305.1961.tb03977.x

[18] H. J. Landau and H. O. Pollak, Bell System Technical Journal, Vol. 41, 1962, pp. 1295-1336.

http://dx.doi.org/10.1002/j.1538-7305.1962.tb03279.x

[19] R Kubo, Reports on Progress in Physics, Vol. 29, 1966, p. 255. http://dx.doi.org/10.1088/0034-4885/29/1/306

[20] J. Haller Jr., Journal of Modern Physics, Vol. 4, 2013, pp. 85-95. http://dx.doi.org/10.4236/jmp.2013.47A1010

[21] J. Haller Jr., Journal of Modern Physics, Vol. 4, 2013, pp. 1393-1399. http://dx.doi.org/10.4236/jmp.2013.410167

[22] E. Nelson, Physical Review, Vol. 150, 1966, pp. 1079-1085. http://dx.doi.org/10.1103/PhysRev.150.1079

[23] S. Chandrasekhar, Reviews of Modern Physics, Vol. 15, 1943, pp. 1-89.

[24] P. A. M. Dirac, “The Principles of Quantum Mechanics,” 4th Edition, Oxford University Press, Oxford, 1958, p. 262.

[25] R. N. Bracewell, “The Fourier Transform and Its Applications,” 2nd Edition, McGraw-Hill Inc., New York, 1986.

[26] I. I. Hirshman Jr., American Journal of Mathematics, Vol. 79, 1957, pp. 152-156.

http://dx.doi.org/10.2307/2372390

[27] H. Nyquist, Physical Review, Vol. 32, 1928, pp. 110-113.

http://dx.doi.org/10.1103/PhysRev.32.110