Maximal Phase Space Compression

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The (seldomly quoted) generalised-Heisenberg uncertainty relations are an effect of the quantum correlation coefficient inequalities. The quantum correlation coefficient determines how much a state can be compacted and on what basis. It is shown that how this can be used to best compress a signal (such as a radio wave, or a 2D laser complex field at a focal plane) while at the same time encrypting the signal.

References

[1] R. Bracewell, “The Autocorrelation Function. The Fourier Transform and Its Applications,” McGraw-Hill, New York, 1965.

[2] W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, “Correlation and Autocorrelation Using the FFT,” In: W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Eds., Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd Edition, Cambridge University Press, Cambridge, 1992, p. 538.

[3] R. Bracewell, “The Fourier Transform and Its Applications,” 3rd Edition, McGraw-Hill, New York, 1999.

[4] G. B. Folland, “Real Analysis: Modern Techniques and their Applications,” 2nd Edition, Wiley, New York, 1999.

[5] E. Schrodinger, “On the Heisenberg(ian) Uncertainty Principle,” Berl. Ber., Vol. 19, 1930, p. 296.

[6] E. Schr?dinger, “Collected Papers Vol. 3: Contributions to Quantum Theory,” Austrian Academy of Sciences, Vienna, 1984, p. 348.

[7] D. Bohm, “Quantum Theory,” Prentice Hall, Upper Saddle River, 1951, p. 199.

[8] E. Merzbacher, “Quantum Mechanics,” 2nd Edition, Wiley, New York, 1970, p. 158.

[9] J. M. Lévy-Leblond, “Correlation of Quantum Properties and the Generalized Heisenberg Inequality,” American Journal of Physics, Vol. 54, No. 2, 1986, p. 135.

[10] L. Goldenberg and L. Vaidman, “Applications of a Simple Quantum Mechanical Formula,” American Journal of Physics, Vol. 64, No. 8, 1996, p. 1059.

[11] R. W. Henry and S. C. Glotzer, “A squeezed State Primer,” American Journal of Physics, Vol. 56, 1988, p. 318.

[12] G. Arfken, “Development of the Fourier Integral, Fourier Transforms—Inversion Theorem, and Fourier Transform of Derivatives,” In: Mathematical Methods for Physicists, 3rd Edition, Academic Press, Orlando, 1985, p. 794.

[13] J. F. James, “A Student’s Guide to Fourier Transforms with Applications in Physics and Engineering,” Cambridge University Press, New York, 1995.