Research ArticleOpen AccessGoogle Scholar indexed
Maximal Phase Space Compression
Institute for Physics and Nuclear Engineering, Bucharest, Romania
Institute for Physics and Nuclear Engineering, Bucharest, Romania
- 1 Institute for Physics and Nuclear Engineering, Bucharest, Romania
- 2 Institute for Physics and Nuclear Engineering, Bucharest, Romania
Journal of Signal and Information Processing·Volume 04 (2013)·Pages 170–172·Published 8 May 2013·DOI10.4236/jsip.2013.42024
Copy link · social · email
Abstract
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.
KeywordsQuantum Compression
- R. Bracewell, “The Autocorrelation Function. The Fourier Transform and Its Applications,” McGraw-Hill, New York, 1965.
- 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.
- R. Bracewell, “The Fourier Transform and Its Applications,” 3rd Edition, McGraw-Hill, New York, 1999.
- G. B. Folland, “Real Analysis: Modern Techniques and their Applications,” 2nd Edition, Wiley, New York, 1999.
- E. Schrodinger, “On the Heisenberg(ian) Uncertainty Principle,” Berl. Ber., Vol. 19, 1930, p. 296.
- E. Schr?dinger, “Collected Papers Vol. 3: Contributions to Quantum Theory,” Austrian Academy of Sciences, Vienna, 1984, p. 348.
- D. Bohm, “Quantum Theory,” Prentice Hall, Upper Saddle River, 1951, p. 199.
- E. Merzbacher, “Quantum Mechanics,” 2nd Edition, Wiley, New York, 1970, p. 158.
- J. M. Lévy-Leblond, “Correlation of Quantum Properties and the Generalized Heisenberg Inequality,” American Journal of Physics, Vol. 54, No. 2, 1986, p. 135.
- L. Goldenberg and L. Vaidman, “Applications of a Simple Quantum Mechanical Formula,” American Journal of Physics, Vol. 64, No. 8, 1996, p. 1059.
- R. W. Henry and S. C. Glotzer, “A squeezed State Primer,” American Journal of Physics, Vol. 56, 1988, p. 318.
- 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.
- J. F. James, “A Student’s Guide to Fourier Transforms with Applications in Physics and Engineering,” Cambridge University Press, New York, 1995.