Comment by AdieuToLogic

The problem is not if a bank can track individual legal tender and associate it with an account holder, but instead if a company which is not a bank (such as a grocery store) could determine same.

In other words, how would a merchant be able to establish a specific $20 USD bill was used by a specific person?

No bank would share this information with an entity other than law enforcement and likely would require a court ordered subpoena to do so.