Explicit pure-state density operator structure for quantum tomography

Abstract

The formulation of region operators named by D. Ellinas and A. J. Bracken [Phys. Rev. A 78, 052106 (2008)], which appears as the phase-space integration corresponding to the straight line over the Wigner operator, is manifestly improved and generalized. By virtue of the technique of integration within ordered (both normally ordered and Weyl ordered) product of operators, we show that the integration involved in the generalized region operator can be directly carried through to completion that leads to the explicit pure-state density operator |u⟩λ,τλ,τ⟨u|, where |u⟩λ,τ makes up the coordinate-momentum intermediate representation. This directly results in that the tomogram of a quantum state |ψ⟩ is just proportional to |⟨u|ψ⟩λ,τ|2, where ⟨u|ψ⟩λ,τ is the wave function of |ψ⟩ in the coordinate-momentum intermediate representation.