I don't even know if quantum is necessary for that. There's already blockchain analysis tools. All you have to do is slip up once and tie a wallet that you didn't want anyone to know about to your identity and then it's relatively easy for those tools to be used to see everything you've done.

I almost paid for something with bitcoin once because they weren't taking anything else. Nothing illegal but also something I wouldn't want the world to know I paid for. I ended up choosing not to because I didn't want that transaction forever stored on the blockchain.