中国物理B ›› 2009, Vol. 18 ›› Issue (9): 3714-3718.doi: 10.1088/1674-1056/18/9/018

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Radon transforms of the Wigner operator on hyperplanes

陈俊华, 范洪义   

  1. Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2008-12-21 修回日期:2009-05-06 出版日期:2009-09-20 发布日期:2009-09-20

Radon transforms of the Wigner operator on hyperplanes

Chen Jun-Hua(陈俊华) and Fan Hong-Yi(范洪义)   

  1. Department of Materials Science and Engineering, University of Science and Technology of China, Hefei 230026, China
  • Received:2008-12-21 Revised:2009-05-06 Online:2009-09-20 Published:2009-09-20

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摘要： The generalization of tomographic maps to hyperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution---a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.

Abstract: The generalization of tomographic maps to hyperplanes is considered. We find that the Radon transform of the Wigner operator in multi-dimensional phase space leads to a normally ordered operator in binomial distribution---a mixed-state density operator. Reconstruction of the Wigner operator is also feasible. The normally ordered form and the Weyl ordered form of the Wigner operator are used in our derivation. The operator quantum tomography theory is expressed in terms of some operator identities, with the merit of revealing the essence of the theory in a simple and concise way.

Key words: Radon transform, Wigner operator, hyperplane IWOP

中图分类号:  (Quantum information)

  • 03.67.-a
02.30.Uu (Integral transforms) 02.50.Ng (Distribution theory and Monte Carlo studies)