Secure Quantum Summation with Two Degrees of Freedom United as a Single Entity

Secure quantum summation (SQS) can summate private data and meanwhile keep their privacy. It plays an essential role in the field of secure multi-party computation. There are a couple of SQS protocols whose quantum resource is single photons in both polarization and spatial-mode degrees of freedom. This kind of SQS protocols has a point in common that they use the two degrees of polarization and spatial-mode in the same way. Instead, this paper taps them in an innovative method, they fulfilling different tasks and forming an organic whole in quantum communication. Compared to the ready sister protocols, this method brings about great benefits: not only maintaining the original communication capacity, but also making the presented protocol simpler and more secure without the need of pre-shared keys to block the intercept-resend attack, because this work makes a full use of its inherent security attributes. Consequently, this work can be considered as a more ideal SQS.