Composably Secure Delegated Quantum Computation with Weak Coherent Pulses

Abstract

A client can delegate a quantum computation to a powerful remote server while ensuring the privacy and the integrity of its computation via Secure Delegated Quantum Computation (SDQC). Thanks to recent results making them noise-robust and resource-efficient, proofs-of-concept implementations of generic SDQC protocols have already been demonstrated. Yet, the requirements for implementing them are still too stringent to go beyond this step while maintaining high security expectations. To further reduce their physical resource cost, we show how to realise SDQC using weak coherent pulses (WCPs) instead of single photons. More precisely, we construct a protocol which guarantees that, among a sufficiently large batch of transmitted WCPs, at least one contained only a single photon. This holds even if the adversary controls the transmittance of the photonic link connecting the client and the server. Our protocol's security is proven in the composable Abstract Cryptography (AC) framework. This batch can then be fed to known quantum privacy amplification techniques to prepare a single secure qubit in the X-Y plane, which can be used in any composable SDQC protocol which relies on the secure preparation of single qubits. Furthermore, the guarantee on the batch of states can also be used for Quantum Key Distribution (QKD) where the privacy amplification step is classical. In doing so, we address a weakness in the standard security proof of the decoy state method. While our protocol can be instantiated with any number of different intensities for the WCPs, using only two intensities already shows improved scaling at low transmittance, thus opening the possibility of increasing the distance between the client and the server.