Quantum Secret Aggregation Utilizing a Network of Agents

Suppose that the renowned spymaster Alice controls a network of spies who all happen to be deployed in different geographical locations. Let us further assume that all spies have managed to get their hands on a small, albeit incomplete by itself, secret, which actually is just a part of a bigger secret. In this work, we consider the following problem: given the above situation, is it possible for the spies to securely transmit all these partial secrets to the spymaster so that they can be combined together in order to reveal the big secret to Alice? We call this problem, which, to the best of our knowledge, is a novel one for the relevant literature, the quantum secret aggregation problem. We propose a protocol, in the form of a quantum game, that addresses this problem in complete generality. Our protocol relies on the use of maximally entangled GHZ tuples, shared among Alice and all her spies. It is the power of entanglement that makes possible the secure transmission of the small partial secrets from the agents to the spymaster. As an additional bonus, entanglement guarantees the security of the protocol, by making it statistically improbable for the notorious eavesdropper Eve to steal the big secret.