Towards higher precision and operational use of optical homodyne tomograms

Abstract

We present the results of an operational use of experimentally measured optical tomograms to determine state characteristics (purity) avoiding any reconstruction of quasiprobabilities. We also develop a natural way how to estimate the errors (including both statistical and systematic ones) by an analysis of the experimental data themselves. Precision of the experiment can be increased by postselecting the data with minimal (systematic) errors. We demonstrate those techniques by considering coherent and photon-added coherent states measured via the time-domain improved homodyne detection. The operational use and precision of the data allowed us to check for the first time purity-dependent uncertainty relations and uncertainty relations for Shannon and Rényi entropies.

11 pages, 6 figures, 1 table, some results are extended

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• Single photon-added coherent states: estimation of parameters and fidelity of the optical homodyne detection
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• Stochastic evolution of finite level systems: classical vs. quantum
• Reliable confidence regions for quantum tomography using distribution moments
• Wigner function and the probability representation of quantum states
• Quantum Uncertainty and Entropy
• Characterizing quantum synchronization in the van der Pol oscillator via tomogram and photon correlation
• Janus-faced tomograms and retrieval of quadrature moments for $q$-deformed states
• An investigation of nonclassical properties of light using an optical tomogram