There are two parts to privacy. One is whether we communicate privately with each other. Then, also, the codes that are used to secure your bank accounts are the same ones that are used for private communication. These encryption methods will have to be upgraded.
Once we have this, for the rest there's not much difference from a privacy point of view from what you have without quantum computers. Whether you have a piece of information that comes from a quantum computer or from a classical computer, it's just information.