Abstract We introduce a generalized algebraic framework for the bright–dark mode decomposition of a two-path quantum interferometer entangled with a path-sensitive detector. Within this formulation, the loss of interference visibility is reinterpreted not as a destruction of quantum coherence, but as a conserved, coherent redistribution of amplitude between a bright (interfering) sector and a dark (path-informative) sector of the joint quanton–detector state. Unlike previous bright–dark formulations restricted to bosonic field-mode algebra in optical or cavity-QED systems, our approach utilizes the universal SU (2) geometry of the two-path Hilbert space. This allows the formalism to be applied to any single-particle ( N = 1) interferometer, including massive fermions such as electrons or neutrons, where particle statistics introduce no additional constraints. We demonstrate that as detector distinguishability increases, amplitude flows continuously and predictably into the dark sector, providing a quantitative redistribution sum rule that governs the transition from interference to which-path information. This algebraic perspective offers a unified, platform-independent language for characterizing decoherence and complementarity, providing a direct operational framework for monitoring information flow in diverse quantum interferometric platforms.
Pacquiao et al. (Sun,) studied this question.