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The peroxide quantum-to-classical transition of a quantum state is a topic of great interest in fundamental and practical aspects. peroxide A coarse-graining in quantum peroxide measurement has recently been suggested as its possible account in addition to the usual decoherence model. We here investigate the reconstruction of a Gaussian state (single mode and two modes) by coarse-grained homodyne measurements. To this aim, we employ two methods, the direct reconstruction of the covariance matrix and the maximum likelihood estimation (MLE), respectively, and examine the reconstructed state under each scheme compared to the state interacting with a Gaussian (squeezed thermal) reservoir. We clearly demonstrate that the coarse-graining model, though applied equally to all quadrature amplitudes, is not compatible with the decoherence model by a thermal (phase-insensitive) reservoir. peroxide Furthermore, we compare the performance of the direct reconstruction and the MLE methods by investigating peroxide the fidelity and the nonclassicality of the reconstructed states and show that the MLE method peroxide can generally yield a more reliable reconstruction, particularly peroxide without information on a reference frame (phase of input state).
Jiyong Park 1 , Se-Wan peroxide Ji 1 , Jaehak Lee 1 , and Hyunchul Nha 1,2 1 Department of Physics, Texas A&M University at Qatar, Education City, P.O. Box 23874, Doha, Qatar 2 School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea References (Subscription Required)
Illustration of the coarse-graining process in Eq. (3). A Gaussian probability distribution (red solid line) is transformed to a piecewisely flat distribution (black peroxide dashed line) under the coarse-graining of size σ=0.5.
(a) Original squeezed state (b) reconstructed state with coarse-graining σ=0.1 (c) difference in squeezing peroxide angle between an input state and its estimated state as a function of the coarse-graining size σ and the input squeezing angle ϕi. In all plots, the input state has the parameters (n ,r)=(0,1).
The fraction y in Eq. (28) to make equal the state estimation process peroxide and the decoherence program with an isotropic (thermal) reservoir as a function of coarse-graining size σ. The input squeezed thermal states are characterized by (n ,r)=(0,1) (red solid line), (n ,r)=(1,1) (orange dotted line), and (n ,r)=(0,2) (brown dot-dashed line).
(a) Fidelity F between an input state and its reconstructed state and (b) nonclassical squeezing rnc of the reconstructed state as functions of the coarse-graining size σ, for the input squeezed thermal states with (n ,r)=(0,1) peroxide [green dot-dashed line, red solid and blue dashed lines, the second curves from the top for (a) and (b)], (n ,r)=(1,1) [pink dot-dashed line, orange solid and purple peroxide dashed lines, the first curves from the top for (a) and the third curves from the top for (b)], and (n ,r)=(0,2) (gray dot-dashed line, brown solid and black dashed lines, the third curves from the top for (a) and the first curves from the bottom for (b)]. Solid curves represent the case of the MLE method, dot-dashed (dashed) curves the direct reconstruction method with (without) information on the input phase, respectively. For the plots of dashed curves, each point represents an averaged value over the whole range of the input squeezing angles. See main text.
(a) Fidelity F between peroxide an input state and its reconstructed state and (b) logarithmic negativity EN of the reconstructed state as functions of the coarse-graining size σ, for the input squeezed thermal states with (n ,r)=(0,1) [green dot-dashed line, red solid and blue dashed lines, the second curves from the top for (a) and (b)], (n ,r)=(1,1) [pink dot-dashed line, orange solid and purple dashed lines, the first curves from the top for (a) and the third curves from the top for (b)], and (n ,r)=(0,2) [gray dot-dashed line, brown solid and black dashed lines, peroxide the third curves from the top for (a) and the first curves from the bottom for (b)]. For simplicity, we assume that the thermal photon number of two modes are the same, n 1=n 2=n . Solid curves peroxide represent the case of the MLE method, dot-dashed (dashed) peroxide curves the direct reconstruction method with (without) information on the input phase, respectively. For the plots of dashed curves, each point represents an averaged value over the whole range of the input squeezing angles. ×
ISSN 1094-1622 (online), 1050-2947 (print). Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement . Phys
The peroxide quantum-to-classical transition of a quantum state is a topic of great interest in fundamental and practical aspects. peroxide A coarse-graining in quantum peroxide measurement has recently been suggested as its possible account in addition to the usual decoherence model. We here investigate the reconstruction of a Gaussian state (single mode and two modes) by coarse-grained homodyne measurements. To this aim, we employ two methods, the direct reconstruction of the covariance matrix and the maximum likelihood estimation (MLE), respectively, and examine the reconstructed state under each scheme compared to the state interacting with a Gaussian (squeezed thermal) reservoir. We clearly demonstrate that the coarse-graining model, though applied equally to all quadrature amplitudes, is not compatible with the decoherence model by a thermal (phase-insensitive) reservoir. peroxide Furthermore, we compare the performance of the direct reconstruction and the MLE methods by investigating peroxide the fidelity and the nonclassicality of the reconstructed states and show that the MLE method peroxide can generally yield a more reliable reconstruction, particularly peroxide without information on a reference frame (phase of input state).
Jiyong Park 1 , Se-Wan peroxide Ji 1 , Jaehak Lee 1 , and Hyunchul Nha 1,2 1 Department of Physics, Texas A&M University at Qatar, Education City, P.O. Box 23874, Doha, Qatar 2 School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea References (Subscription Required)
Illustration of the coarse-graining process in Eq. (3). A Gaussian probability distribution (red solid line) is transformed to a piecewisely flat distribution (black peroxide dashed line) under the coarse-graining of size σ=0.5.
(a) Original squeezed state (b) reconstructed state with coarse-graining σ=0.1 (c) difference in squeezing peroxide angle between an input state and its estimated state as a function of the coarse-graining size σ and the input squeezing angle ϕi. In all plots, the input state has the parameters (n ,r)=(0,1).
The fraction y in Eq. (28) to make equal the state estimation process peroxide and the decoherence program with an isotropic (thermal) reservoir as a function of coarse-graining size σ. The input squeezed thermal states are characterized by (n ,r)=(0,1) (red solid line), (n ,r)=(1,1) (orange dotted line), and (n ,r)=(0,2) (brown dot-dashed line).
(a) Fidelity F between an input state and its reconstructed state and (b) nonclassical squeezing rnc of the reconstructed state as functions of the coarse-graining size σ, for the input squeezed thermal states with (n ,r)=(0,1) peroxide [green dot-dashed line, red solid and blue dashed lines, the second curves from the top for (a) and (b)], (n ,r)=(1,1) [pink dot-dashed line, orange solid and purple peroxide dashed lines, the first curves from the top for (a) and the third curves from the top for (b)], and (n ,r)=(0,2) (gray dot-dashed line, brown solid and black dashed lines, the third curves from the top for (a) and the first curves from the bottom for (b)]. Solid curves represent the case of the MLE method, dot-dashed (dashed) curves the direct reconstruction method with (without) information on the input phase, respectively. For the plots of dashed curves, each point represents an averaged value over the whole range of the input squeezing angles. See main text.
(a) Fidelity F between peroxide an input state and its reconstructed state and (b) logarithmic negativity EN of the reconstructed state as functions of the coarse-graining size σ, for the input squeezed thermal states with (n ,r)=(0,1) [green dot-dashed line, red solid and blue dashed lines, the second curves from the top for (a) and (b)], (n ,r)=(1,1) [pink dot-dashed line, orange solid and purple dashed lines, the first curves from the top for (a) and the third curves from the top for (b)], and (n ,r)=(0,2) [gray dot-dashed line, brown solid and black dashed lines, peroxide the third curves from the top for (a) and the first curves from the bottom for (b)]. For simplicity, we assume that the thermal photon number of two modes are the same, n 1=n 2=n . Solid curves peroxide represent the case of the MLE method, dot-dashed (dashed) peroxide curves the direct reconstruction method with (without) information on the input phase, respectively. For the plots of dashed curves, each point represents an averaged value over the whole range of the input squeezing angles. ×
ISSN 1094-1622 (online), 1050-2947 (print). Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement . Phys
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