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arXiv:0907.3345 · Optics Express

Photostatistics reconstruction via loop detector signatures

James Webb, Elanor H. Huntington

Published Jul 2, 2009• 8 citations

Abstract

Photon-number resolving detectors are a fundamental building-block of optical quantum information processing protocols. A loop detector, combined with appropriate statistical processing, can be used to convert a binary on/off photon counter into a photon-number-resolving detector. Here we describe the idea of a signature of photon-counts, which may be used to more robustly reconstruct the photon number distribution of a quantum state. The methodology is applied experimentally in a 9-port loop detector operating at a telecommunications wavelength and compared directly to the approach whereby only the number of photon-counts is used to reconstruct the input distribution. The signature approach is shown to be more robust against calibration errors, exhibit reduced statistical uncertainty, and reduced reliance on a-priori assumptions about the input state.

DOI: 10.1364/oe.17.011799

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Many present day quantum optics experiments, particularly in optical quantum information processing, rely on number-resolving photo-detection as a basic building block. In this paper we demonstrate that a simple classical optimisation technique can sometimes be employed to post-process the detector signature and improve the confidence of the measurement outcome in the presence of photon-number errors such as loss or dark-counts. While the regime in which this technique is applicable is rather restrictive, and will likely not be very useful for the large-scale quantum information processing applications of the future, the ideas presented might be employed in some present-day experiments where photo-detectors are typically very poor.

Characterizing the input-output photon-number distribution of an unknown optical quantum channel is a worthwhile task for many applications in quantum information processing. Ideally, this would require deterministic photon-number sources and photon-number-resolving detectors, but these technologies are still work in progress. In this work, we propose a general method to rigorously bound the input-output photon-number distribution of an unknown optical channel using standard optical devices such as coherent light sources and non-photon-number-resolving detectors and homodyne detectors. To demonstrate the broad utility of our method, we consider the security analysis of practical quantum key distribution systems based on calibrated single-photon detectors and an experimental proposal to implement time-correlated single-photon counting technology using homodyne detectors instead of single-photon detectors.

The photon number distribution is reconstructed from the measured statistics of vacuum states in single-photon detection. Numerical results are presented for the coherent, thermal, number and squeezed-vacuum states. The quantum efficiency of single-photon detection should be high for the successful evaluation of the number state. The quantum efficiency provides the marginal influence for the evaluation of the coherent, thermal and squeezed-vacuum states. However, the accuracy of the reconstructed photon number distribution of the squeezed-vacuum state is low even though the quantum efficiency is unity. For a more accurate reconstruction, we must obtain a priori information on the photon number distribution of the squeezed-vacuum state.

We study the properties of a photodetector that has a numberresolving capability. In the absence of dark counts, due to its finite quantum efficiency, photodetection with such a detector can only eliminate the possibility that the incident field corresponds to a number of photons less than the detected photon number. We show that such a non-photon number-discriminating detector, however, provides a useful tool in the reconstruction of the photon number distribution of the incident field even in the presence of dark counts.