When dealing with composite systems comprising a finite subsystem and an infinite one, the aim often involves numerically analyzing specific properties, such as entanglement entropy between these subsystems.

In the process of performing a partial trace over one of the subsystems, which approach yields more reliable results: tracing over the finite system or over an approximation of the infinite subsystem? Intuitively, tracing over the larger subsystem seems preferable since it reduces the dimensionality of the remaining matrix. However, does this reasoning hold when considering the faithfulness of the results?