Consider the following:

db.test.insert({a: {b:2}})
db.test.ensureIndex({
    'a.b': 1
  }, {
    name: 'test_index',
    background: true,
    partialFilterExpression: {
      'a': { $exists: true }
    }
  })

db.test.find({'a.b': 2}).explain(true)

Actual:
The index is not used (the first execution stage of the explain(true) result is COLLSCAN

Expected:
The index is used and IXSCAN shows up in the explain(true) results. This seems logic since the query `'a.b': 1` implies `'a':

`.