Database sharing in Private Information Retrieval (PIR)
Information theoretic PIR protocols that have communication complexity less than the size of the database require multiple, non-cooperating servers [1]. In a computational setting, this is not required. So if you do not want to have to share your database with multiple servers, you should probably use a computational PIR protocol.

1. https://en.wikipedia.org/wiki/Private_information_retrieval#Advances_in_information_theoretic_PIR