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arXiv:1711.07153 · Optics Letters

Robustness of quantum Fourier transform interferometry

Bogdan Opanchuk, Laura Rosales-Zárate, M. D. Reid, P. D. Drummond

Published Jan 9, 2019• 11 citations
arXivHTMLPDF

Abstract

We analyze the effect of decoherence and noise on quantum Fourier transform interferometry, in which a boson sampling photonic network is used to measure optical phase gradients. This novel type of metrology is shown to be robust against phase decoherence. One can also measure gradients using lower-order correlations without substantial degradation. Our results involve the estimation of up to a 100×100 matrix permanent.

DOI
10.1364/ol.44.000343

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Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for quantum Fourier transform over the intrinsic decoherence-free subspaces. The scheme is then applied to the circuit design of quantum Fourier transform over quantum networks under collective decoherence. The encoding efficiency and possible improvements are also discussed.
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We show that the quantum Cram\'er-Rao bound on the error of measurement of the optical phase gradient with a beam of finite width (or the wavefront tilt within a finite aperture) is consistent with the Fourier-transform uncertainty principle for the single-photon state, and is a factor of NNN lower for the maximally entangled NNN-photon state. This fundamental bound therefore governs the tradeoff between quantum sensitivity and spatial resolution. Error bounds for a structured configuration using binary projective-field measurements implemented by an image-inversion (II) interferometer are higher, and the factor of NNN advantage attained by the NNN-photon maximally entangled state is reduced and eventually washed out as the beam width or the phase gradient increases. This reduction is more rapid for larger NNN, so that the quantum advantage is more vulnerable. The precision of the II interferometer is greater than that based on a split detector placed in the focal plane of a lens.
Abstract In the domain of quantum metrology, cat states have demonstrated their utility despite their inherent fragility with respect to losses. Here, we introduce noise robust optical cat states which exhibit a metrological robustness for phase estimation in the regime of high photon numbers. These cat states are obtained from the intense laser driven process of high harmonic generation (HHG), and show a resilience against photon losses. Focusing on a realistic scenario including experimental imperfections we opt for the case in which we can maximize the lower bound of the quantum Fisher information (QFI) instead of analyzing the best case scenario. We show that the decrease of the QFI in the lossy case is suppressed for the HHG-cat state compared to the even and odd counterparts. In the regime of small losses of just a single photon, the HHG-cat state remains almost pure while the even/odd cat state counterparts rapidly decohere to the maximally mixed state. More importantly, this translates to a significantly enhanced robustness for the HHG-cat against photon loss, demonstrating that high photon number optical cat states can indeed be used for metrological applications even in the presence of losses.