Private property (as opposed to personal property) is property owned by individuals or entities that generate profits from others’ labor, and is abolished under communism. So, no, you can’t take someone’s personal PC (or any personal property). I’m not that deep into communist theory or thought, so not sure if “free markets” can exist under communism (I know money and states don’t exist), but I know there are theoretical socialist societies where free markets exist (market socialism, anarcho-syndicalism, etc).