Did Peter receive the keys of the kingdom uniquely, or did all the apostles receive them?

Only Peter received the keys. Jesus said, to you I give the keys of the kingdom, and whatever you bind on earth shall be bound in heaven, in Matthew 16:19, and that you is a Greek singular. In Matthew 18:18 the binding and loosing is given to all the apostles, but they do not have the keys. That means Peter is the head, the one who makes the final decision. You see it already in Acts chapter 1, where they have to replace Judas, and Peter is the one who stands up and says here is what we will do, using Psalm 109:8. At Pentecost Peter is the lead spokesman for all the apostles, quoting Joel to the Jews. In Acts 3 he heals the man at the temple gate. And in Acts 15, at the first council in Jerusalem, when they are arguing about whether Christians should be circumcised, Peter says no, and that settles it, and then they discuss how to implement Peter's decision. So it is not only Matthew 16, it is Acts 1 through 15; Peter was the top dog, and that is what the keys are about. Jesus knew what He was doing when He gave Peter the keys, because otherwise everybody thinks something different and you can never come to a final decision.