You can redesign your schema like this:
{
pairs:[
{k: "a", v: 5775},
{k: "b", v: "b1"},
]
}
Then you indexing your key:
db.people.ensureIndex({"pairs.k" : 1})
After this you will able to search by exact match:
db.ent.find({'pairs.k':"a"})
In case you go with Sparse index and your current schema, proposed by @WesFreeman, you will need to create an index on each key you want to search. It can affect write performance or will be not acceptable if your keys are not static.
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