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arXiv:quant-ph/9901064 · Physical Review A

Quantum homodyne tomography with a priori constraints

Konrad Banaszek

Published Jun 1, 1999• 18 citations
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Abstract

I present an iterative algorithm for reconstructing the Wigner function from homodyne statistics. The proposed method, based on maximum-likelihood estimation, is capable of compensating for detection losses in a numerically stable way.
DOI
10.1103/physreva.59.4797

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We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an O((1/k)log⁡D)O ( ( 1 / k ) \log D )O((1/k)logD) rate, where kkk denotes the number of iterations and DDD denotes the dimension of the quantum state. The per-iteration computational complexity of the algorithm is O(D3+ND2)O ( D ^ 3 + N D ^2 )O(D3+ND2), where NNN denotes the number of measurement outcomes. The algorithm can be considered as a parameter-free correction of the RρRR ρRRρR method [A. I. Lvovsky. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. \textit{J. Opt. B: Quantum Semiclass. Opt.} 2004] [G. Molina-Terriza et al. Triggered qutrits for quantum communication protocols. \textit{Phys. Rev. Lett.} 2004.].