Multi-Photon Multi-Channel Interferometry for Quantum Information Processing
Abstract
This thesis reports advances in the theory of design, characterization and simulation of multi- photon multi-channel interferometers. I advance the design of interferometers through an algorithm to realize an arbitrary discrete unitary transformation on the combined spatial and internal degrees of freedom of light. This procedure effects an arbitrary n_s n_p × n_s n_p unitary matrix on the state of light in n_s spatial and n_p internal modes. The number of beam splitters required to realize a unitary transformation is reduced as compared to existing realization by a factor n_p^2/2. I thus enable the optical implementation of higher dimensional unitary transformations.
I devise an accurate and precise procedure for characterizing any multi-port linear optical interferometer using one- and two-photon interference. Accuracy is achieved by estimating and correcting systematic errors that arise due to spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision are attained by fitting experimental coincidence data to a curve simulated using measured source spectra. The efficacy of our characterization procedure is verified by numerical simulations.
I develop group-theoretic methods for the analysis and simulation of linear interferometers. I devise a graph-theoretic algorithm to construct the boson realizations of the canonical SU(n) basis states, which reduce the canonical subgroup chain, for arbitrary n. The boson realizations are employed to construct D-functions, which are the matrix elements of arbitrary irreducible representations, of SU(n) in the canonical basis. I show that immanants of principal submatrices of a unitary matrix T are a sum Σ_tD^{(λ)}_{tt}(Ω) of the diagonal D-functions of group element Ω, with t determined by the choice of submatrix, and the irrep (λ) determined by the immanant under consideration. The algorithm for SU(n) D-function computation and the results connecting these functions with immanants open the possibility of group-theoretic analysis and simulation of linear optics.
Description
Keywords
Optics, Physics--Theory
Citation
Dhand, I. (2015). Multi-Photon Multi-Channel Interferometry for Quantum Information Processing (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27032