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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 perfect detectors.There exists a small λ-μ region within which optimal unbiased covariance-matrix estimators obtained with homodyne detection are more accurate than those obtained with heterodyne. In typical experimental conditions where Gaussian states prepared can neither give rise to minimum uncertainties nor be truely coherent states, there exist a plethora of settings for which .
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f4: Surface plots of the performance ratio for perfect detectors.There exists a small λ-μ region within which optimal unbiased covariance-matrix estimators obtained with homodyne detection are more accurate than those obtained with heterodyne. In typical experimental conditions where Gaussian states prepared can neither give rise to minimum uncertainties nor be truely coherent states, there exist a plethora of settings for which .

Mentions: To analyze the consequence of this quantum-mechanical uncertainty, we use the correct expressions for GHOM and GHET and first consider the ideal situation where the detections are perfect (η = 1). Figure 4 shows the surface plot generated for Eq. (4). From the plot, we note the maximal influence on γ as a manifestion of the Arthurs-Kelly uncertainty for minimum-uncertainty states (μ = 1), where . The tomographic accuracy associated with heterodyne detection takes the worst-case magnitude for coherent states and remains greater than unity for all squeezed states (λ > 1). For Gaussian states of higher temperatures (μ > 1) that are sufficiently squeezed, γ would eventually be smaller than unity, since in the range λ ≫ 1, it can be shown that the gradient of in λ is always steeper than that of . The ratio γ approaches unity as λ goes to infinity for all μ, in agreement with the previous discussion above.


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 perfect detectors.There exists a small λ-μ region within which optimal unbiased covariance-matrix estimators obtained with homodyne detection are more accurate than those obtained with heterodyne. In typical experimental conditions where Gaussian states prepared can neither give rise to minimum uncertainties nor be truely coherent states, there exist a plethora of settings for which .
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Surface plots of the performance ratio for perfect detectors.There exists a small λ-μ region within which optimal unbiased covariance-matrix estimators obtained with homodyne detection are more accurate than those obtained with heterodyne. In typical experimental conditions where Gaussian states prepared can neither give rise to minimum uncertainties nor be truely coherent states, there exist a plethora of settings for which .
Mentions: To analyze the consequence of this quantum-mechanical uncertainty, we use the correct expressions for GHOM and GHET and first consider the ideal situation where the detections are perfect (η = 1). Figure 4 shows the surface plot generated for Eq. (4). From the plot, we note the maximal influence on γ as a manifestion of the Arthurs-Kelly uncertainty for minimum-uncertainty states (μ = 1), where . The tomographic accuracy associated with heterodyne detection takes the worst-case magnitude for coherent states and remains greater than unity for all squeezed states (λ > 1). For Gaussian states of higher temperatures (μ > 1) that are sufficiently squeezed, γ would eventually be smaller than unity, since in the range λ ≫ 1, it can be shown that the gradient of in λ is always steeper than that of . The ratio γ approaches unity as λ goes to infinity for all μ, in agreement with the previous discussion above.

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.