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Multi-Database Quantum Symmetric Private Information Retrieval without Shared Randomness
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==Outline== <!-- A non-mathematical detailed outline which provides a rough idea of the concerned protocol --> ''A user wants to privately retrieve an element from a classical database that has been replicated and distributed among <math>k</math> servers. Servers do not want the user to get any information on the database beyond the desired database item.'' *'''Query:''' First, the user hides the index of the desired database element in several classical queries (one per server) and using some randomness. Then, the user prepares one quantum register (‘query register’) per server that depends on the classical query, on some new randomness (one per server) and on some function of the index of the desired database element and the randomness of the classical queries (which will be useful in the retrieval phase). Those quantum registers are entangled with another qubit kept by the user, and then sent to the user. *'''Answer:''' Each server applies some unitary map on the received query register and sends the resulting register (‘answer register’) back to the client. The classical answer of a given server is encoded in the corresponding answer register. *'''Retrieval:''' From all the received answer registers, the user can retrieve the desired database element: the user disentangles the answer registers from his qubit, then applies a Hadamard transform to his qubit and measures it in the computational basis. The outcome of the measurement is the desired database element.
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