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Quantum Information and Measurement (QIM)

Quantum-State Tomography with Photon-Number-Resolving Homodyne Detection

Stefano Olivares, Alessia Allevi, Matteo G. A. Paris, Maria Bondani

Published Jan 1, 2019• 1 citation
Publisher

Abstract

A homodyne-like detection scheme based on photon-number-resolving and low-intensity a local oscillator is exploited to reconstruct optical quantum states by applying the same tomographic reconstruction procedures originally developed for standard homodyne detection based on photodiodes.
DOI
10.1364/qim.2019.s4b.2

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Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
Abstract We address state reconstruction by photon-number-resolving detectors, and demonstrate that they may be effectively exploited to perform quantum tomography of states of light. In particular, we find that the pattern function technique, originally developed for optical homodyne tomography, may be also applied to discrete data. Our results open new perspectives for quantum-state reconstruction in the mesoscopic regime, and pave the way to the use of photon-number-resolving-based detection schemes in Quantum Information science.
The measurement of quantum states of light is fundamental for the investigations of Quantum Optics and for the applications of Quantum Information. Here we present the implementation of a novel detection apparatus, that is a homodyne-like detection scheme based on photon-number-resolving detectors. Thanks to its hybrid nature, the apparatus is useful to investigate both the particle-like and wave-like properties of light. We tested the scheme in the measurement of the quadratures of different optical states, namely coherent states and mixtures of coherent states. In particular, we investigate the performance of our scheme compared to that of a standard homodyne detector.
Optical homodyne tomography consists in reconstructing the quantum state of an optical field from repeated measurements of its amplitude at different field phases (homodyne data). The experimental noise, which unavoidably affects the homodyne data, leads to a detection efficiency η<1\eta<1η<1 . The problem of reconstructing quantum states from noisy homodyne data sets prompted an intense scientific debate about the presence or absence of a lower homodyne efficiency bound ( η>0.5\eta> 0.5η>0.5 ) below which quantum features, like quantum interferences, cannot be retrieved. Here, by numerical experiments, we demonstrate that quantum interferences can be effectively reconstructed also for low homodyne detection efficiency. In particular, we address the challenging case of a Schrödinger cat state and test the minimax and adaptive Wigner function reconstruction technique by processing homodyne data distributed according to the chosen state but with an efficiency η<0.5\eta< 0.5η<0.5 . By numerically reproducing the Schrödinger’s cat interference pattern, we give evidence that quantum state reconstruction is actually possible in these conditions, and provide a guideline for handling optical tomography based on homodyne data collected by low efficiency detectors.