Distortion correction for free-space quantum communication

Abstract

The work in this thesis can be put into two categories: First, the effect of atmospheric turbulence on single-photon optical fields and on quantum entangled orbital angular momentum(OAM)systemsisassessed. Secondly,themitigationagainsttheeffectsof atmospheric turbulence on OAM based quantum systems is considered. In the first part, the evolution of single-photon optical fields propagating through atmospheric turbulence is studied under arbitrary turbulence conditions. The single phasescreen(SPS)modelandtheinfinitesimalpropagationequation(IPE)areusedto compute the optical power fractions in an input Laguerre-Gaussian (LG) mode. The power fractions transferred to high-order LG modes are also computed. The study showsthatwhileunderweakscintillationconditionstheIPEandtheSPSmodelsshow thesametrend,theydeviatewhenthestrengthofscintillationreachesacertainthreshold. Theabovecomputationsaresubsequentlycomparedwithnumericalsimulations of optical fields propagating through atmospheric turbulence. The numerical simulations are performed in accordance with the multi-phase screen (MPS) model based on the Kolmogorov theory of turbulence. The simulations are performed for different turbulence strengths to allow for comparison in both weak and strong scintillation. ThenumericalresultsareinagreementwiththeIPEresultsforallconditions,butthey deviate from the SPS results for weak scintillation. Further,aspartofthefirstcategory,theeffectoftheatmosphericturbulenceonsecondorderquantuminterferenceintheHong-Ou-Mandel(HOM)effectisinvestigated. The investigation involves a theoretical and experimental analysis. In the experiment, quantum states that are entangled in the orbital angular momentum (OAM) degree of freedom are prepared with spontaneous parametric downconversion (SPDC). The atmospheric turbulence, which is modeled in accordance with the SPS approach, is simulated with spatial light modulators according to the Kolmogorov theory of turbulence. Both the theoretical and experimental analyses show that the HOM dip is unaffected when only one of the photons passes through atmospheric turbulence. However, it is observed that when both photons are sent through the atmospheric turbulence, the HOM is only slightly affected. The second part of the thesis starts with the proposal of a method for characterizing a high-dimensional quantum channel with the aid of classical light. The method uses a single non-separable input optical field that contains correlations between the spatial modes (OAM) and the wavelength degrees of freedom. The channel estimationprocessincorporatesthespontaneousparametricupconversionorsumfrequency generation to perform the pertinent measurements. Finally, singular value thresholding (SVT) based compressive sensing is used to perform high dimensional quantum channel estimation. The estimated channel is subsequently used to correct for the turbulence induced distortion on the input quantum state. As a measure of the success of the procedure, the fidelity and trace distance of the corrected density matrix against the ideal maximally entangled qutrit state is computed. The results are compared with those of the uncorrected density matrix. Furthermore, the amount of entanglement is quantified using both the corrected and the uncorrected density matrices.