Evolution of decoherence in a two-mode entangled system under amplitude decay

Based on our recently published work [Front. Phys. 21, 093201 (2026)], we extend the analysis to the density-operator evolution of a two-mode entangled quantum system subject to amplitude decay and show that the output state retains the same functional structure as the initial density operator throughout the decay. We further examine the evolutions of several quantum statistical distributions and the von Neumann entropy used to quantify entanglement during the process. This work offers a systematic approach to studying two-mode entangled open systems and yields results on the von Neumann entropy that may help facilitate entanglement measurement.