All of a sudden the bank has created money several times over. But technology marches on. We also have the theoretical capability of making cash in forms other than green paper or round metal slices. We can make cash live in a smart card, for example, or in your computer, on the Internet, as digital cash. Complicating the question is the recognition that even today's greenbacks are not completely anonymous.
Paper money has traceable serial numbers.
In the near future, cash registers could automatically scan and record those serial numbers while unobtrusively snapping a photograph of your face. In the slightly more distant future, it might be simple to do a DNA analysis of the bills to see who's been handling them. In either case, a network of merchants, corporations, and government agencies sharing this information could trace the movement of your cash through the economy. Computers are extremely flexible. It's a well-known axiom that they do only what their programmers tell them to do.