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There's no such thing as a communist state. There have been plenty of dictatorships of the proletariats, but communism requires the state to have already been abolished. And no, you can't own something in a communist state. Everything is given from those with ability to those with need. If you don't have a right to something, you can't own it. It's more like the government leasing it to you in return for labor, at least until said government is abolished.
Communism's end goal is also anarchy but I can't see how you'd redistribute according to people's needs without some sort of bureaucracy, which goes right back into statism.
As for Elm's claim that "at least there's examples of communist states", the only examples are the Kropotkin sort of "anarcho-communism" — Makhnovia, Revolutionary Catalonia, etc. — and I guess it's worth noting that they all fell to external threats rather than internal collapse. On the other hand, if you're talking about examples of Marxist communism, there's none.