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28 March 2024
 
  » arxiv » 1908.3404

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Probability representation of quantum dynamics using pseudo-stochastic maps
E.O. Kiktenko ; A.O. Malyshev ; A.S. Mastiukova ; V.I. Man'ko ; A.K. Fedorov ; D. Chruściński ;
Date 9 Aug 2019
AbstractIn this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems using pseudo-stochastic maps acting on probability distributions obtained via symmetric informationally complete positive operator-valued measure (SIC-POVM). These true probability distributions that fully describe quantum states can be directly accessible in an experiment. We provide stochastic representation both for unitary evolution of the density matrix governed by the von Neumann equation and dissipative evolution governed by Markovian master equation. Finally, we reconstruct experimentally a pseudo-stochastic matrix of a single-qubit gate on the IBM quantum processor. Within performing the experiment we develop a method of employing SIC-POVM measurements, which allows eliminating read-out errors inherent to single-qubit projective measurements. This forms a link between our results on the representation of quantum channels using pseudo-stochastic maps and practical tasks of improving the accuracy of the reconstruction of quantum states and channels in existing quantum devices.
Source arXiv, 1908.3404
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