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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.


Surface plots of the performance ratio for various detector efficiencies.Here, Arthurs-Kelly uncertainty is neglected in heterodyne detection. The rate of increase in the ratio γ is slightly sensitive to the value of η, with the effective λ-μ region in which heterodyne detection significantly outperforms homodyne detection reduces as η increases.
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f3: Surface plots of the performance ratio for various detector efficiencies.Here, Arthurs-Kelly uncertainty is neglected in heterodyne detection. The rate of increase in the ratio γ is slightly sensitive to the value of η, with the effective λ-μ region in which heterodyne detection significantly outperforms homodyne detection reduces as η increases.

Mentions: To gain insights in the fundamental difference between homodyne and heterodyne detection, let us first consider the hypothetical situation where there are no quantum-mechanical consequences in simultaneously measuring two incompatible observables — the absence of all Arthurs-Kelly-type uncertainties. This entails the equalities and GHOM = GHET for the detector-efficiency terms and covariance matrices. The ratio is then a monotonically increasing function of λ, μ and η. It turns out that this function has a maximum value of one, which is attained in the limit λ, μ → ∞. The ratio γ is smallest when λ = μ = 1, taking the minimal value of 3/10 for all minimum-uncertainty states (μ = 1) with circular Wigner-function profiles (λ = 1), i.e. the coherent states. Extreme elongation of the profiles as a result of huge photonic quadrature squeezing (λ ≫ 1) renders both CV schemes equivalent in tomographic performance since the significant regions of sampling approach phase-space lines of infinite length, and details of the two schemes in this hypothetical setting are irrelevant within such infinitesimally thin regions. Figure 3 illustrates all the observations made.


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

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

Surface plots of the performance ratio for various detector efficiencies.Here, Arthurs-Kelly uncertainty is neglected in heterodyne detection. The rate of increase in the ratio γ is slightly sensitive to the value of η, with the effective λ-μ region in which heterodyne detection significantly outperforms homodyne detection reduces as η increases.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Surface plots of the performance ratio for various detector efficiencies.Here, Arthurs-Kelly uncertainty is neglected in heterodyne detection. The rate of increase in the ratio γ is slightly sensitive to the value of η, with the effective λ-μ region in which heterodyne detection significantly outperforms homodyne detection reduces as η increases.
Mentions: To gain insights in the fundamental difference between homodyne and heterodyne detection, let us first consider the hypothetical situation where there are no quantum-mechanical consequences in simultaneously measuring two incompatible observables — the absence of all Arthurs-Kelly-type uncertainties. This entails the equalities and GHOM = GHET for the detector-efficiency terms and covariance matrices. The ratio is then a monotonically increasing function of λ, μ and η. It turns out that this function has a maximum value of one, which is attained in the limit λ, μ → ∞. The ratio γ is smallest when λ = μ = 1, taking the minimal value of 3/10 for all minimum-uncertainty states (μ = 1) with circular Wigner-function profiles (λ = 1), i.e. the coherent states. Extreme elongation of the profiles as a result of huge photonic quadrature squeezing (λ ≫ 1) renders both CV schemes equivalent in tomographic performance since the significant regions of sampling approach phase-space lines of infinite length, and details of the two schemes in this hypothetical setting are irrelevant within such infinitesimally thin regions. Figure 3 illustrates all the observations made.

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.