Sum rules in multiphoton coincidence rates

Abstract

We show that sums of carefully chosen coincidence rates in a multiphoton interferometry experiment can be simplified by replacing the original unitary scattering matrix with a coset matrix containing $0$s. The number and placement of these $0$s reduces the complexity of each term in the sum without affecting the original sum of rates. In particular, the evaluation of sums of modulus squared of permanents is shown to turn in some cases into a sum of modulus squared of determinants. The sums of rates are shown to be equivalent to the removal of some optical elements in the interferometer.

arXiv commentPost publication version which includes minor typos fixes and clarifications. 21 pages, 3 figures

References in corpus (15)

• Sampling of partially distinguishable bosons and the relation to the multidimensional permanent
• Partial indistinguishability theory for multi-photon experiments in multiport devices
• Generalised Hong-Ou-Mandel Experiments with Bosons and Fermions
• Direct dialling of Haar random unitary matrices
• Simple factorization of unitary transformations
• Representations of the Weyl group and Wigner functions for SU(3)
• Permanents in linear optical networks
• SU(3) Quantum Interferometry with single-photon input pulses
• The sinh-Gordon defect matrix generalized for n defects
• The Canonical Coset Decomposition of Unitary Matrices Through Householder Transformations
• Permutational symmetries for coincidence rates in multi-mode multi-photonic interferometry
• Complexity and Completeness of Immanants
• D-functions and immanants of unitary matrices and submatrices
• Determinant and Permanent of Hessenberg Matrix and Generalized Lucas Polynomials
• Coincidence landscapes for polarized bosons