Phase-noise induced many-body interference suppression in Gaussian Boson Sampling

Abstract

We develop a Heisenberg-picture tensor-network formulation of collision-free Gaussian Boson Sampling, providing a direct Fock-space expression for output probabilities in terms of experimentally accessible quantities. The resulting representation naturally recovers the Hafnian structure while revealing the decomposition of GBS probability into a phase-insensitive contribution and a hierarchy of interference sectors associated with pairs of perfect matchings. As an application, we investigate phase diffusion and show how it progressively suppresses many-body interference, driving the output statistics toward a classical dimer-model regime. Our results establish a transparent framework for connecting experimentally characterized phase fluctuations with the loss of quantum interference in photonic quantum sampling experiments.