Reconstruction of Wigner Functions on Different Observation Levels
The Wigner function  of the quantum-mechanical state which is described by the density operator ρ can, in principle, be reconstructed either via a set of the single observable measurements (the so called optical homodyne tomography [2,3]) or via a simultaneous measurement of two non-commuting observables (see for instance a concept of propensities as discussed by Wódkiewicz  and others [5,6]) The completely reconstructed Wigner function, or equivalently, the reconstructed density operator, contains information about all independent moments of the system operators, i.e., in the case of the quantum harmonic oscillator the knowledge of the Wigner function is equivalent to the knowledge of all moments 〈(â†) m â n 〉 of the creation ( â † ) and annihilation ( â ) operators.
KeywordsPure State Density Operator Wigner Function Photon Number Observation Level
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