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arXiv · 1706.07816

Quantitative tomography for continuous variable quantum systems

Olivier Landon-Cardinal·Luke C. G. Govia·Aashish A. Clerk
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Abstract

We present a continuous variable tomography scheme that reconstructs the Husimi Q-function (Wigner function) by Lagrange interpolation, using measurements of the Q-function (Wigner function) at the Padua points, the optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasi-linear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q-function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

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Olivier Landon-Cardinal, Luke C. G. Govia, Aashish A. Clerk. 2017-06-23. Quantitative tomography for continuous variable quantum systems. https://doi.org/10.1103/physrevlett.120.090501

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