Quantum conference key agreement using photonic graph state
Joseph Ho (Heriot-Watt University);
Alex Pickston (Heriot-Watt University);
Francesco Graffitti (Heriot-Watt University);
Federico Grasselli (Heinrich Heine University Dusseldorf);
Chris L Morrison (Heriot-Watt University);
Massimiliano Proietti (Heriot-Watt University);
Andres Ulibarrena (Heriot-Watt University);
Alessandro Fedrizzi (Heriot-Watt University)
Abstract: Quantum conference key agreement (CKA) is a cryptographic task for sharing a secret common key between multiple users. CKA has been established as a network protocol that can leverage multipartite entanglement (NQKD) to gain an advantage over contemporary two-party communication primitives (2QKD). Specifically, when performing QCKA in constrained quantum networks, e.g., with limited channel capacities, NQKD schemes can produce the conference key between N users with up to an N-1 rate advantage over 2QKD. QCKA has previously been implemented by direct transmission of a 4-photon GHZ state, however did not show the advantage comparison. Here we show this advantage using a universal network resource represented by a 6-qubit photonic graph state.
Abstract: Coherent-one-way (COW) quantum key distribution (QKD) held the promise of distributing secret keys over long distances with a simple experimental setup while being robust against the photon-number splitting attack. Indeed, there are already commercial products implementing this scheme, and long distance realizations over 300 km have been reported recently. Surprisingly enough, however, here we show that its asymptotic secret key rate scales at most quadratically with the system's transmittance, thus solving a long standing problem. This means that COW is actually inappropriate for long distance QKD transmission. This is done by deriving the optimal zero-error attack, which is a type of attack where the eavesdropper does not introduce any error, but still prevents Alice and Bob from distilling a secure key. In doing so, we also show, for instance, that all implementations of the COW scheme reported so far in the scientific literature are insecure.
Abstract: The rates of several device-independent (DI) protocols, including quantum key-distribution (QKD) and randomness expansion (RE), can be computed via an optimization of the conditional von Neumann entropy over a particular class of quantum states. In this work we introduce a numerical method to compute lower bounds on such rates. Our rate calculations are valid for systems on general separable Hilbert spaces and we also investigate the convergence of our method to the actual rate, proving convergence in certain situations. Applying our method to compute the rates of DI-RE and DI-QKD protocols we find substantial improvements over all previous numerical techniques, demonstrating significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD we show a new minimal detection efficiency threshold which is within the realm of current capabilities. Moreover, we demonstrate that our method is able to converge rapidly by recovering instances of all known tight analytical bounds. Finally, we note that our method is compatible with the entropy accumulation theorem and can thus be used to compute rates of finite round protocols and subsequently prove their security.