Quantitative tomography for continuous variable quantum systems

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.

4.25 pages, 2 figures (+ 3.5 pages, 4 figures)

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• Classification and reconstruction of optical quantum states with deep neural networks
• Detector-Agnostic Phase-Space Distributions
• Direct Characteristic-Function Tomography of the Quantum States of Quantum Fields
• Demonstrating efficient and robust bosonic state reconstruction via optimized excitation counting
• Response in violation of Bell inequality to imperfect photon addition and subtraction in noisy squeezed states of light
• Gradient-descent methods for fast quantum state tomography
• Entropic distinguishability of quantum fields in phase space
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• Phase space distributions in information theory
• Experimental demonstration of enhanced quantum tomography via quantum reservoir processing
• Out-of-distribution generalisation for learning quantum channels with low-energy coherent states
• Pulse characterization at the single-photon level through chronocyclic $Q$-function measurements
• Witnesses of Genuine Multipartite Entanglement and Nonlocal Measurement Back-action for Raman-scattering Quantum Systems
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises