All information traveling through these apps is anonymous and this measure is only a temporary public safety move. It cannot possibly give rise to a police state when no personal identifiers are mentioned. The way these apps collect data is by Bluetooth. When someone's phone is in the range of another device, those devices can receive signals from each other. Due to this type of communication, massive amount of personal information are not shared. Also, any app in collaboration with the government would need to pass privacy laws. Such solutions will help restart the economy without putting lives in danger.
The benefits to these technologies far outweigh the overblown negatives. Imagine getting a text that could save someone's life and the lives of their loved ones. Even if it did mean sacrificing a little personal data, isn't life more important than data? Would dying really be worth the few bits of personal information that the government--sworn to protect its citizens, including their personal data--might get?
Then there's the fact that enforcing a lockdown could also lead to a police state. In an extreme case, one might not even be allowed to leave their home. Personal freedom is going to be at risk no matter what, because a global pandemic is such a dire situation that it calls for dire actions and solutions. So either way, lockdown or no lockdown, a "police state" would be inevitable if survival is valued above personal freedoms--which is, truthfully, how it should be. A temporary sacrifice of personal freedoms is nothing compared to the permanent sacrifice of a life.