Godt spørsmål!
The answer to that is Romans 13:3-4, which reads: "For rulers are not a terror to good conduct, but to bad. Would you have no fear of the one who is in authority? Then do what is good, and you will receive his approval, for he is God's servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God's wrath on the wrongdoer."
So the sword belongs to the government. Now, in what capacity it can or should be used can be debated, and it can also be abused. However, generally and practically speaking, a Christian can serve in a nation that has capital punishment or one that doesn't — either way with a clear conscience. He is not sinning in obeying the government in either case.