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• W3100916092 endingPage "075017" @default.
• W3100916092 startingPage "075017" @default.
• W3100916092 abstract "In the framework of noisy quantum homodyne tomography with efficiency parameter $1/2 < eta leq 1$, we propose a novel estimator of a quantum state whose density matrix elements $rho_{m,n}$ decrease like $Ce^{-B(m+n)^{r/ 2}}$, for fixed $Cgeq 1$, $B>0$ and $0<rleq 2$. On the contrary to previous works, we focus on the case where $r$, $C$ and $B$ are unknown. The procedure estimates the matrix coefficients by a projection method on the pattern functions, and then by soft-thresholding the estimated coefficients. We prove that under the $mathbb{L}_2$ -loss our procedure is adaptive rate-optimal, in the sense that it achieves the same rate of conversgence as the best possible procedure relying on the knowledge of $(r,B,C)$. Finite sample behaviour of our adaptive procedure are explored through numerical experiments." @default.
• W3100916092 created "2020-11-23" @default.
• W3100916092 creator A5058651667 @default.
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• W3100916092 date "2013-06-24" @default.
• W3100916092 modified "2023-10-15" @default.
• W3100916092 title "Adaptive estimation of the density matrix in quantum homodyne tomography with noisy data" @default.
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• W3100916092 doi "https://doi.org/10.1088/0266-5611/29/7/075017" @default.
• W3100916092 hasPublicationYear "2013" @default.
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