Distortions produced in optical homodyne tomography

An analysis of the homodyne tomography process that is often used to determine the Wigner functions of quantum optical states is performed to consider the effects of the spatiotemporal degrees of freedom. The homodyne tomography process removes those parts of the input state that are not associated with the mode of the local oscillator by tracing out those degrees of freedom. Using a functional approach to incorporate all the spatiotemporal degrees of freedom, we find that this reduction in the degrees of freedom introduces distortions in the observed Wigner function. The analysis also shows how the homodyne tomography process introduces a resolution that depends on the strength of the local oscillator. As examples, we consider coherent states, Fock states and squeezed vacuum states.

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