Quasi-trusted relays for quantum networks

Le Quoc Cuong, Patrick Bellot

We examine a timely and important topic in quantum information, computation, and communication. The utility of quantum key distribution (QKD) will depend on the ability to establish large networks of securely connected sites. Current implementations based on sending and receiving single photos have considerable constraints on the range at which secure cryptographic channels can be established. Proposed solutions involved entanglement swapping have severe technological challenges, namely the storage of quantum states.

We have proposed a new untrusted qauntum relay model. The key element is a C-NOT gate implemented at each relay node. In essence, the C-NOT and subsequent measurement serve as a Bell measurement. In the QQTB and QQTR models, it may be possible to unfold the protocol, just like the Shor-Preskill proof of the security of BB84, and relate it to E91. The role of the Bell measurement at the relay could be seen to entangle Alice and Bob in the same sense of Shor-Preskill. The QQTR model suffers from exactly the same problems as normal entanglement relays, namely the difficulty in performing a deterministic Bell measurement on photons. A fixed finite probability of performing each intermediate measurement leads to exponentially decreasing rate with range since the protocol requires simultaneous success in the absence of local storage.We have extended the quasi trusted model to untrusted intermediate nodes. We have studied the precise relation of the untrusted relay model to conventional entanglement swapping. The device proposed as the core of the relay is essentially the same as in entanglement swapping (being a Bell measurement). This leads naturally to issues of the comparative advantages and disadvantages as well as the question of whether both models can be mapped onto each other.

1. Le Quoc Cuong. “Innovative models for quantum networks”, Télécom ParisTech, PhD Thesis, november 2010.
2. Le Quoc Cuong et Patrick Bellot. “How Can Quasi-Trusted Nodes Help to Secrurely Relay QKD Keys”. International Journal of Network Security,  vol. 9, n. 3,  pp. 233-241, November 2009.
3. Le Quoc Cuong et Patrick Bellot. “A novel approach to build QKD relaying models”. Wiley’s International Journal of Security and Communication Networks, accepted August 2009.
4. Le Quoc Cuong and Patrick Bellot. “A new proposal for QKD relaying models”. 17th International Conference on Computer Communications and Networks (ICCCN 08), St. Thomas U.S. Virgin Island (USA),  August 2008.
5. Le Quoc Cuong and Patrick Bellot. “How to use the quantum XOR gate as a relay to extend the QKD range ?”. 4th International Workshop on Boolean Functions: Cryptography and Applications (BFCA 08),  Copenhague (Danemark), May 2008.