Weyl Ordering, s-Ordering, Quantum Phase Operator and Radon Transform of Wigner Operator

Ke Zhang, Chengyu Fan, Hong-Yi Fan

Dominik Bayer, Elena Cordero, Karlheinz Gröchenig +1 more

Junhua Chen, Fan Hong‐Yi

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.

Fang Jia, Haoliang Zhang, Liyun Hu +1 more

FANHong-Yi

Based on the technique of integral within a Weyl ordered product of operators, wc present applicationsof the Weyl ordered two-mode Wigner operator for quantum mechanical entangled system, e.g., we derive the complex Wigner transform and its relation to the complex fractional Fourier transform, as well as the entangled Radon transform.

Fan Hong‐Yi

Based on the technique of integral within a Weyl ordered product of operators, we present applications of the Weyl ordered two-mode Wigner operator for quantum mechanical entangled system, e.g., we derive the complex Wigner transform and its relation to the complex fractional Fourier transform, as well as the entangled Radon transform.