Re-identifying your social network from contact trace&test decentralised apps

Obviously, some people are uncomfortable about the app that holds your contact data for the purposes of helping warn people they may have been infected, so have devised decentralised apps to achieve same goal. however, they kind of miss the obvious. 

There's no point in the app unless people act on notifications. acting entails i) isolating ii) getting tested so if negative, can stop isolating as soon as possible. if positive, can get treatment.

If you don't want to act on notifications, don't run the app.

So now what happens when a contactee is tested?

A simple re-identification of people is do-able 

if the case rate is low and largely localized.

So if patient A is first new person on day D tested +ve in city C, and then their set of decentralized possibly infected folks F are notified and  go and get tested, and say this shuts down the outbreak, then the testing agency knows that the set of F people are contacts of A. It doesn't get too much harder to do this probalistically if there's a slightly bigger outbreak with a few As and Fs in a city/locale, based on timing...

If the case is high and not localized, contact tracing and testing has failed, and we are in a second wave. and there are lots more dead people.

So centralised or decentralised, you have to trust the test center people. who (in the NHS case) are basically the same people.