Memory loss is contagious in open quantum systems

Memoryless (Markovian) system-bath interactions are of fundamental interest in physics. While typically, the absence of memory originates from the characteristics of the bath, here we demonstrate that it can result from the system becoming lossy due to the Markovian interaction with a second bath. This uncovers an interesting interplay between independent baths and suggests that Markovianity is ``contagious'', i.e., it can be transferred from one bath to another through the system with which they both interact. We introduce a Bloch-Redfield-inspired approach that accounts for this distinct origin of Markovianity and uniquely combines non-Hermitian Hamiltonian formalism with master equations. This method significantly improves the description of the interaction between a lossy system (associated with a Lindblad master equation) and a non-Markovian bath, reducing the computational demands of complex system-bath setups across various fields.