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Kluwer Academic Publishers eBooks

Accuracy in Quantum Homodyne Tomography

Giacomo Mauro D’Ariano, Chiara Macchiavello, Nicoletta Sterpi

Published Dec 19, 2005• 0 citations
Publisher

Abstract

We study the statistical errors in homodyne tomography of radiation density matrix in the photon number representation. We give an asymptotic estimate for large matrix indexes at different values of the quantum efficiency η of homodyne detectors. We show that for fixed η the errors increase exponentially as functions of the matrix index.

DOI
10.1007/0-306-47097-7_24

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We study the statistical errors in homodyne tomography of radiation density matrix in the photon number representation. We give an asymptotic estimate for large matrix indexes at different values of the quantum efficiency η of homodyne detectors. We show that for fixed η the errors increase exponentially as functions of the matrix index.
We study both systematic and statistical errors in radiation density matrix measurements. First we estimate the minimum number of scanning phases needed to reduce systematic errors to below a fixed threshold. Then, we calculate the statistical errors, intrinsic in the procedure that gives the density matrix. We present a detailed study of such errors versus the detectors' quantum efficiency and the matrix indices in the number representation, for different radiation states. For unit quantum efficiency, and for both coherent and squeezed states, the statistical errors of the diagonal matrix elements saturate for large n. In contrast, off-diagonal errors increase with the distance from the diagonal. For non-unit quantum efficiency the statistical errors along the diagonal do not saturate and increase dramatically versus both and the matrix indices.
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