  Realizing Majorana bound states (MBSs) in short, well-controllable chains of
coupled quantum dots sidesteps the problem of disorder, but requires
fine-tuning and does not give the true topological protection inherent to long
chains. Here, we introduce a new quality measure that is applicable also in the
presence of strong electron-electron interactions and that quantifies the
closeness to topological protection of finetuned MBSs in short quantum-dot
chains. We call this measure local distinguishability because it puts a bound
to the degree an arbitrary local measurement can distinguish between two
states. We study the local distinguishability for quantum-dot chains of
different length. The three-dot chain is studied in detail, and we find that it
may not always be an improvement over the two-dot case, a fact that can be
understood within an effective model derived from perturbation theory. For
longer chains, the local distinguishability vanishes exponentially, signalling
a transition to a topological phase with two ground states that cannot be
distinguished by any local measurement.
