  Recently, entropy corrections on nonorientable manifolds such as the Klein
bottle are proposed as a universal characterization of critical systems with an
emergent conformal field theory (CFT). We show that entropy correction on the
Klein bottle can be interpreted as a boundary effect via transforming the Klein
bottle into an orientable manifold with nonlocal boundary interactions. The
interpretation reveals the conceptual connection of the Klein bottle entropy
with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a
generic scheme to extract these universal boundary entropies from quantum Monte
Carlo calculation of partition function ratios in lattice models. Our numerical
results on the Affleck-Ludwig entropy and Klein bottle entropy for the
$q$-state quantum Potts chains with $q=2,3$ show excellent agreement with the
CFT predictions. For the quantum Potts chain with $q=4$, the Klein bottle
entropy slightly deviates from the CFT prediction, which is possibly due to
marginally irrelevant terms in the low-energy effective theory.
