Finite number of measurements in optical homodyne tomography

For infinite dimensional quantum systems, no general theory exists of the effect of using a finite size ensemble in quantum state measurements. We approach this topic by considering one particular measurement scheme, optical homodyne tomography. We define a measure which tells us how well a quantum state, belonging to a pre-set state space, is determined after N measurements. We illustrate the method by considering, as an example, a state space which includes all coherent and squeezed states as well as certain superpositions of these.