This isn't good:
The Pepp-Pt or Pan-European Privacy-Preserving Proximity Tracing is a project whose aim is to provide a framework for developing national automated contact tracing tools to help societies test more intelligently so as to return to normalcy as soon as possible without risking the COVID-19 epidemic flaring up again and overwhelming ICU capabilities.
It would be possible to do it in a decentralized manner by having the contact data stored only the users' local devices. The phone apps could be programmed to broadcast their owners pseudonym+status after testing so that others in the contact network could see if they have a reason to seek out testing. The broadcasting could be done only authorized by a code given to them by a healthcare practitioner who administers the test. This would have to be in place to prevent spamming and broadcasting deliberate false positives to hurt the network. Such a system, while not being able to automatically generate the maximum amount of data readily available for epidemiological modelers would be very useful. Also, it would be impossible to enforce quarantine measures upon anybody.
Many involved now question the initiative and have announced they will withdraw from it citing that they are not doing so not only because of the risk of the system being repurposed for state surveillance later but because decentralization is necessary to convince people to partake in the system in the first place. I think that's a valid point.