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Optica Publishing Group
  • Quantum Electronics and Laser Science Conference
  • OSA Technical Digest (Optica Publishing Group, 2001),
  • paper QThN2

Quantum State Reconstruction: A comparison of Maximum Likelihood and Tomographic Schemes

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Abstract

For some time now experimental techniques for the measurement of the quantum state of light have been the subject of intensive investigation.1 Tomographic techniques have been applied to experiments such as the homodyne measurement of the Wigner function of a single mode of light2 and of the density matrix of the polarization degrees of freedom of a pair of entangled photons.3 In this technique the density matrix (or Wigner function) which characterizes the quantum state of the system being measured is found from a linear transformation of experimental data. There are a number of drawbacks to the method, principally in that the recovered state might not, because of experimental noise, correspond to a physical state. For example, density matrices for any quantum state must be Hermitian, positive semi-definite matrices with unit trace. The tomo- graphically measured matrices often fail to be positive semi-definite.

© 2001 Optical Society of America

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