That's a small wrench:
Random citizen Randy who does not try to anonimize carries a 10$ bill will hence call Randy's bill
Random citizen Rachel who also doesn't try to anonimize carries a 5$ bill.
Both carry phones gossiping location history to surveillance state. If any of those bills are brought to a bank by some seller, neither Randy nor Rachel will have visited the sellers store recently, so the spooks know it switched hands.
Find any consumption place (bar/shop/...) which both Randy and Rachel have visited "shortly" after each other (location history), since they were last known to carry the bill.
They apparently both went to the same bar.
1) You better not carry your cellphone when anonimizing your 20$ dollar bill in the bar.
2) You better (in the bar) not be within the "light cones" of 2 events: going absent from your phone (forward speed cone), rejoining your phone (reverse speed cone). So locomote very fast!
1) and 2) frustrate each other,
better just don't own a phone.
Your phone can detect from noise, motion (accelerometer/gyro),etc if its owner has left it behind or returns, and you will be one of only few people in a large radius who is not carrying his phone like a good boy.
They are not directly interested in tracking Randy and Rachel, they track them to track those who anonymize.
They are not directly interested in tracking you probably, they track you to track the hard targets. When most substantial (i.e. bills) money flows are fully explained, only a sparse amount of bill transmissions, and a sparse amount of suspicious behaviours need to be matched.
EDIT:
1) When you anonimize a large bill by splitting it, and you get multiple bills back, you must destroy the lower amount bills. (EDIT 2: CORRECTION better keep it and leave it on a train, different trains for each superfluous bill)
2) Lets pretend the introduction of smartphones was the start of surveillance state, say 15 years ago. Individually we have potentially 15 man-years of experience with surveillance, on the other hand a 250 million population nation state has 15*250 million man-years of experience with surveillance!
3) Given a sequence of hypothetical events, it is easy for me to attack a known strategy, but how can the state collect anonymizing strategies? "Easy" : for each flawless execution of anonymization, there will be hundreds of flawed executions: a person not realizing he shouldnt carry a smartphone but correctly splitting his bill after ATM: if enough cases like this are found, you can try find other patterns in their common behaviour, for example after using the anonymized $10 bill on whatever, doesnt see harm in using the extra $5 bill (in conjunction with say his phone, or in conjunction with a fresh $20 bill from ATM)
From all the known (but failed) attempts, we can try and look for alternative ways we could have anonymized them. Some will turn out to be aware of other side-channels and will have found original remedies for one problem, introducing a second sidechannel, which can be taken into account in the future