Quantum tomograms from intermediate entangled states

Xiang‐Guo Meng, Ji‐Suo Wang, Bao‐Long Liang

E. Nahvifard, M. R. Bazrafkan

Vladimir I. Man’ko, Giuseppe Marmo, Alberto Simoni +2 more

Chuanmei Xie, Hong-Yi Fan

Based on the Fan—Hu's formalism, i.e., the tomogram of two-mode quantum states can be considered as the module square of the states' wave function in the intermediate representation, which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating the quantum tomogram of two-mode density operators, i.e., the tomogram of a two-mode density operator is equal to the marginal integration of the classical Weyl correspondence function of F 2 † ρ F 2 , where F 2 is the two-mode Fresnel operator. An application of the theorem in evaluating the tomogram of an optical chaotic field is also presented.

Xiang‐Gao Meng, Ji‐Suo Wang, Bao‐Long Liang +1 more

Optical tomogram of a quantum state can serve as an alternative to its density matrix since it contains all the information on this state. In this paper we use the explicit expression of the intermediate state | q, f , g〉(that is, an eigenvector of the coordinate and momentum operator fQ + gP ) and the Radon transform between the Wigner operator Δ(p, q) and the pure-state density operator | q, f, g 〉〈 q, f, g | to calculate the specific tomograms for multiple-photon-added coherent states (MPACSs), thermal states (MPATSs) and displaced thermal states (MPADTSs). Their analytical tomograms are actually the finite-summation representations related to single-variable Hermite polynomials. Besides, the numerical results indicate that the larger photon-addition number can lead to the multi-peak tomographic distributions for these three states, and the measurable tomograms of MPACSs and MPADTSs exhibit π-periodic features but MPATSs can’t.

I. A. Howard, Norman Henry March