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arXiv:quant-ph/9910085 · Physical Review A

Universal homodyne tomography with a single local oscillator

Giacomo Mauro D’Ariano, Massimiliano Federico Sacchi, Prem Kumar

Published Dec 13, 1999• 29 citations
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Abstract

We propose a general method for measuring an arbitrary observable of a multimode electromagnetic field using homodyne detection with a single local oscillator. In this method the local oscillator scans over all possible linear combinations of the modes. The case of two modes is analyzed in detail and the feasibility of the measurement is studied on the basis of Monte Carlo simulations. We also provide an application of this method in tomographic testing of the Greenberger-Horne-Zeilinger state.

DOI
10.1103/physreva.61.013806

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We propose a general method for measuring an arbitrary observable of a multimode electromagnetic field using homodyne detection with a single local oscillator. In this method the local oscillator scans over all possible linear combinations of the modes. The case of two modes is analyzed in detail and the feasibility of the measurement is studied on the basis of Monte Carlo simulations. We also provide an application of this method in tomographic testing of the Greenberger-Horne-Zeilinger state.
We consider multimode homodyne tomography with a single local oscillator and derive sampling functions for multimode s-parametrized quasidistributions and s-ordered moments of creation and annihilation operators. In both cases, loss-compensating sampling functions, applicable to realistic measurement with imperfect detection, are provided. Results of Monte Carlo simulations for a squeezed three-mode state are reported and the feasibility of reconstruction of the three-mode Q function from 107{10}^{7}107 sampled data points is demonstrated.
Homodyne tomography - i. e. homodyning while scanning the local oscillator phase - is now a well assessed method for ``measuring'' the quantum state. In this paper I will show how it can be used as a kind of universal detection, for measuring generic field operators, however at expense of some additional noise. The general class of field operators that can be measured in this way is presented, and includes also operators that are inaccessible to heterodyne detection. The noise from tomographical homodyning is compared to that from heterodyning, for those operators that can be measured in both ways. It turns out that for some operators homodyning is better than heterodyning when the mean photon number is sufficiently small. Finally, the robustness of the method to additive phase-insensitive noise is analyzed. It is shown that just half photon of thermal noise would spoil the measurement completely.
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