Step 1: Understanding the Question:
Population density = population divided by area (persons per sq. km); north-eastern hill states generally have very low densities due to rugged terrain and small populations.
Step 2: Compare known densities (Census 2011, persons/sq.km):
Arunachal Pradesh \(\approx 17\); Mizoram \(\approx 52\); Himachal Pradesh \(\approx 123\); Nagaland \(\approx 119\).
Step 3: Pick the lowest:
Among these four, Arunachal Pradesh has by far the lowest density — it is in fact the least densely populated state in mainland India.
Step 4: Final Answer:
\[ \boxed{\text{Arunachal Pradesh}} \]