Triggered Qutrits for Quantum Communication Protocols

Abstract

A general protocol in quantum information and communication relies in the ability of producing, transmitting, and reconstructing, in general, qunits. In this Letter we show for the first time the experimental implementation of these three basic steps on a pure state in a three-dimensional space, by means of the orbital angular momentum of the photons. The reconstruction of the qutrit is performed with tomographic techniques and a maximum-likelihood estimation method. For the tomographic reconstruction we used more than 2400 different projections. In this way we also demonstrate that we can perform any transformation in the three-dimensional space.

Diluted maximum-likelihood algorithm for quantum tomography

“…For ǫ → ∞, the iteration becomes that of Ref. [13,14]. On the other hand, we prove that the likelihood will increase in every iteration step for ǫ → 0.…”

“…[13,14]. A generic tomographic measurement is described by a positive-operator-valued measure (POVM), with the outcome of the j'th measurement associated with a specific positive operatorΠ j ≥ 0, with jΠ j normalized to the identity operator.…”

“…An alternative algorithm described below, which takes advantage of the structure of the MaxLik reconstruction problem and has good convergence properties was proposed by [12] and later adapted to different physical systems such as external degrees of freedom of a photon [13] and the optical harmonic oscilla-tor [14]. Thanks to its good properties, this method has been widely used in recent experiments on optical homodyne tomography of both single-and multimode optical states [15].…”

Helicity and angular momentum: A symmetry-based framework for the study of light-matter interactions

“…Finally, it is worth noting that expressions (4) and (5) can be interpreted and computed as a weighted average. When the electromagnetic field is decomposed in a basis of eigenvectors of J z , the total integrated value J z is equal to a weighted average [19, chap.…”

“…From experimental astrophysics proposals for the detection of exotic cosmic objects [1] to the use of light beams to rotate atoms [2], through the exploitation of the infinite number of possible angular momentum values for increasing the capacity of optical communication networks [3] or developing new concepts in quantum information [4].…”