Photon-Number Tomography of Multimode States and Positivity of the Density Matrix

@article{Manko2003PhotonNumberTO,
  title={Photon-Number Tomography of Multimode States and Positivity of the Density Matrix},
  author={Olga V. Man'ko and Vladimir I. Man'ko},
  journal={Journal of Russian Laser Research},
  year={2003},
  volume={24},
  pages={497-506}
}
For one-mode and multimode light, the photon-number tomograms of Gaussian quantum states are explicitly calculated in terms of multivariable Hermite polynomials. Positivity of the tomograms is shown to be a necessary condition for positivity of the density matrix. 
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9 Citations

9 Citations

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References

SHOWING 1-10 OF 13 REFERENCES
Phys
  • Rev., 177, 1882
  • 1969
Found
  • C. Ross
  • Medicine
    The Dental register
  • 1869
Phys
  • Rev. A, 40, 2847
  • 1989
V
  • I. Man’ko, and P. Tombesi, Europhys. Lett., 37, 79
  • 1997
Phys
  • Rev. Lett., 70, 1244
  • 1993
Phys
  • Rev. Lett., 76, 4344
  • 1996
O
  • V. Man’ko, V. I. Man’ko, Yu. F. Smirnov, and V. N. Tolstoy, J. Phys. A: Math. Gen., 35, 6101
  • 2002
Soc
  • Am. B, 4, 1715
  • 1987
O
  • V. Man’ko, and V. I. Man’ko, Phys. Rev. A, 49, 2993
  • 1994
Phys
  • Rev. A, 36, 5866
  • 1987
...
...