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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.


Marginal and conditional uncertainties of a joint distribution function.For a joint distribution function over a two-variable (two-dimensional) space, the marginal variance for data sampled along a particular reference direction (indicated by a double-headed arrow) can be understood as a shadow cast from the joint uncertainty region in the orthogonal direction (indicated by the corresponding perpendicular pair of dashed lines). On the other hand, the conditional variance is directly obtained by slicing the joint uncertainty region about its center along the same reference direction. The marginal uncertainty region is the region defined by pairs of points bounding the marginal variances in all directions, which is similar to how the conditional uncertainty region is related to the conditional variances.
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f2: Marginal and conditional uncertainties of a joint distribution function.For a joint distribution function over a two-variable (two-dimensional) space, the marginal variance for data sampled along a particular reference direction (indicated by a double-headed arrow) can be understood as a shadow cast from the joint uncertainty region in the orthogonal direction (indicated by the corresponding perpendicular pair of dashed lines). On the other hand, the conditional variance is directly obtained by slicing the joint uncertainty region about its center along the same reference direction. The marginal uncertainty region is the region defined by pairs of points bounding the marginal variances in all directions, which is similar to how the conditional uncertainty region is related to the conditional variances.

Mentions: Figure 2 illustrates this point for a Gaussian joint distribution function and the proof is straightforward. Let us consider a Gaussian conditional probability distribution of two random variables characterized by a two-dimensional covariance matrix G, and denote the marginal variance by , and the conditional variance by . We shall fix the reference direction, defined by the angle θ and shown graphically as dashed straight lines in Fig. 2, along which we choose to either average/integrate over (marginal variance) or slice (conditional variance), to be parallel to the basis vector .


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

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

Marginal and conditional uncertainties of a joint distribution function.For a joint distribution function over a two-variable (two-dimensional) space, the marginal variance for data sampled along a particular reference direction (indicated by a double-headed arrow) can be understood as a shadow cast from the joint uncertainty region in the orthogonal direction (indicated by the corresponding perpendicular pair of dashed lines). On the other hand, the conditional variance is directly obtained by slicing the joint uncertainty region about its center along the same reference direction. The marginal uncertainty region is the region defined by pairs of points bounding the marginal variances in all directions, which is similar to how the conditional uncertainty region is related to the conditional variances.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Marginal and conditional uncertainties of a joint distribution function.For a joint distribution function over a two-variable (two-dimensional) space, the marginal variance for data sampled along a particular reference direction (indicated by a double-headed arrow) can be understood as a shadow cast from the joint uncertainty region in the orthogonal direction (indicated by the corresponding perpendicular pair of dashed lines). On the other hand, the conditional variance is directly obtained by slicing the joint uncertainty region about its center along the same reference direction. The marginal uncertainty region is the region defined by pairs of points bounding the marginal variances in all directions, which is similar to how the conditional uncertainty region is related to the conditional variances.
Mentions: Figure 2 illustrates this point for a Gaussian joint distribution function and the proof is straightforward. Let us consider a Gaussian conditional probability distribution of two random variables characterized by a two-dimensional covariance matrix G, and denote the marginal variance by , and the conditional variance by . We shall fix the reference direction, defined by the angle θ and shown graphically as dashed straight lines in Fig. 2, along which we choose to either average/integrate over (marginal variance) or slice (conditional variance), to be parallel to the basis vector .

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.