Theory of Quantum Computation, Communication, and Cryptography, 4th Workshop, TQC 2009, Waterloo, Canada, May 11-13, 2009, Revised Selected Papers

The problem of memory checking considers storing files on an unreliable public server whose memory can be modified by a malicious party. The main task is to design an online memory checker with the capability to verify that the information on the server has not been corrupted. To store n bits of public information, the memory checker has s private reliable bits for verification purpose; while to retrieve each bit of public information the checker communicates t bits with the public memory. Earlier work showed that, for classical memory checkers, the lower bound s× t ∈ Ω(n) holds. In this article we study quantum memory checkers that have s private qubits and that are allowed to quantum query the public memory using t qubits. We prove an exponential improvement over the classical setting by showing the existence of a quantum checker that, using quantum fingerprints, requires only s ∈ O(logn) qubits of local memory and t ∈ O(polylogn) qubits of communication with the public memory.