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Surmounting intrinsic quantum-measurement uncertainties in Gaussian-state tomography with quadrature squeezing.

Řeháček J, Teo YS, Hradil Z, Wallentowitz S - Sci Rep (2015)

Bottom Line: We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H.Yuen and J.In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.

View Article: PubMed Central - PubMed

Affiliation: Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic.

ABSTRACT
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.

No MeSH data available.


Uncertainty-ellipse reconstruction in phase space.The uncertainty ellipses plotted are reconstructions from particular sets of data that are respectively from measuring N = 50 (red), 100 (green) and 150 (blue) copies or sampling events in phase space, which are compared to the true uncertainty ellipse (black, dashed). The true Gaussian squeezed state considered here is characterized by the parameters μ = 2 and λ = 10, with the detection efficiency η = 0.5. The thickness of each closed curve is proportional to the distance between the reconstructed ellipse and the true ellipse. These plots are representatives of the average performance of the two schemes, a signature of the existence of a wide range of settings for which heterodyne detection is tomographically better than homodyne detection even for moderate values of N.
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f6: Uncertainty-ellipse reconstruction in phase space.The uncertainty ellipses plotted are reconstructions from particular sets of data that are respectively from measuring N = 50 (red), 100 (green) and 150 (blue) copies or sampling events in phase space, which are compared to the true uncertainty ellipse (black, dashed). The true Gaussian squeezed state considered here is characterized by the parameters μ = 2 and λ = 10, with the detection efficiency η = 0.5. The thickness of each closed curve is proportional to the distance between the reconstructed ellipse and the true ellipse. These plots are representatives of the average performance of the two schemes, a signature of the existence of a wide range of settings for which heterodyne detection is tomographically better than homodyne detection even for moderate values of N.

Mentions: In practice, detections are never perfect due to losses, which implies that the detector efficiency η is always less than unity. The surface plots for γ, as shown in Fig. 5, correspondingly possess rather different shapes and curvatures for different values of η. The response to η for homodyne and heterodyne tomography schemes turn out to be quite different. For example, in the limit of very small efficiency, η ≪ 1, the additional η-dependent factor for the heterodyne scheme is almost twice as big as the factor for the homodyne scheme. One should expect homodyne tomography to perform better in this limit. Notice that for realistic detection efficiencies in the range 0.2 < η < 0.8, heterodyne tomography always outperforms homodyne tomography except for a small range of μ and λ parameters. Figure 6 illustrates the performance of the two schemes in terms of uncertainty-ellipse reconstructions of a Gaussian source. Details of its generation are given in Methods.


Surmounting intrinsic quantum-measurement uncertainties in Gaussian-state tomography with quadrature squeezing.

Řeháček J, Teo YS, Hradil Z, Wallentowitz S - Sci Rep (2015)

Uncertainty-ellipse reconstruction in phase space.The uncertainty ellipses plotted are reconstructions from particular sets of data that are respectively from measuring N = 50 (red), 100 (green) and 150 (blue) copies or sampling events in phase space, which are compared to the true uncertainty ellipse (black, dashed). The true Gaussian squeezed state considered here is characterized by the parameters μ = 2 and λ = 10, with the detection efficiency η = 0.5. The thickness of each closed curve is proportional to the distance between the reconstructed ellipse and the true ellipse. These plots are representatives of the average performance of the two schemes, a signature of the existence of a wide range of settings for which heterodyne detection is tomographically better than homodyne detection even for moderate values of N.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4508669&req=5

f6: Uncertainty-ellipse reconstruction in phase space.The uncertainty ellipses plotted are reconstructions from particular sets of data that are respectively from measuring N = 50 (red), 100 (green) and 150 (blue) copies or sampling events in phase space, which are compared to the true uncertainty ellipse (black, dashed). The true Gaussian squeezed state considered here is characterized by the parameters μ = 2 and λ = 10, with the detection efficiency η = 0.5. The thickness of each closed curve is proportional to the distance between the reconstructed ellipse and the true ellipse. These plots are representatives of the average performance of the two schemes, a signature of the existence of a wide range of settings for which heterodyne detection is tomographically better than homodyne detection even for moderate values of N.
Mentions: In practice, detections are never perfect due to losses, which implies that the detector efficiency η is always less than unity. The surface plots for γ, as shown in Fig. 5, correspondingly possess rather different shapes and curvatures for different values of η. The response to η for homodyne and heterodyne tomography schemes turn out to be quite different. For example, in the limit of very small efficiency, η ≪ 1, the additional η-dependent factor for the heterodyne scheme is almost twice as big as the factor for the homodyne scheme. One should expect homodyne tomography to perform better in this limit. Notice that for realistic detection efficiencies in the range 0.2 < η < 0.8, heterodyne tomography always outperforms homodyne tomography except for a small range of μ and λ parameters. Figure 6 illustrates the performance of the two schemes in terms of uncertainty-ellipse reconstructions of a Gaussian source. Details of its generation are given in Methods.

Bottom Line: We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H.Yuen and J.In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.

View Article: PubMed Central - PubMed

Affiliation: Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic.

ABSTRACT
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.

No MeSH data available.