Abstract
In this paper, a theoretical framework is proposed to formulate the quantum interference inside the coupled waveguides with unequal losses. The quantum coupled mode equation is added with the Langevin noise terms to account for the impact of unequal losses, which can be solved analytically. A close form formula is derived for the correlation matrix of the Langevin noise terms, which provides full information for the density matrix of the propagation state. The theory is self-consistent and tested with a three-waveguide system, which is considered as anti-parity-time (PT) symmetric and simulated in the previous publications. An 89-waveguide system is analyzed afterwards to further demonstrate the applicability of the theory.
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