Quantum Online Memory Checking

TL;DR

This paper introduces a quantum memory checker that significantly reduces private memory and communication requirements compared to classical methods by leveraging quantum fingerprints, achieving exponential improvements.

Contribution

The paper demonstrates the first exponential improvement in quantum memory checking, reducing private memory to logarithmic size and communication to polylogarithmic size using quantum techniques.

Findings

Quantum checkers require only O(log n) private qubits.

Communication complexity is reduced to O(polylog n) qubits.

Achieves exponential improvement over classical bounds.

Abstract

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 \in Omega(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 \in O(log n) qubits of local memory and t \in O(polylog n) qubits of communication with the public memory.