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 measuremen ts. We approach this topic by considering one particular measurement s cheme, optical homodyne tomography. We define a measure which tells us how well a quantum state, belonging to a pre-set state space, is dete rmined 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.