The Physical Underpinnings of Privacy

Jean Christian Boileau, University of Toronto

One of the outstanding features of quantum mechanics is the existence of multipartite physical states, known as private states, that upon measurement produce a shared random outcome that cannot in any circumstance be correlated to an external system. Any quantum key distribution (QKD) protocol is in fact an non-coherent version of a private state distillation protocol using decoupled bit and phase error correction codes. To establish the security of a QKD protocol, it is sufficient to construct the latter. However, the most general security proofs avoid a direct correspondence with private state distillation protocol. Inspired by Koashi's complementarity scenario, I'll give an alternative definition of private state in term of an information tradeoff between conjugate bases and then exploit this definition to present a general private state distillation protocol based on CSS codes that achieves the same key rate as recent, more information-theoretic approaches. Additionally, the same method can be used to establish the hashing inequality for entanglement distillation, as well as the direct part of the quantum coding theorem. I also discuss a generalization of the Maassen-Uffink entropic uncertainty relation, its connection to our new definition of private state and possible applications to security analysis. If time permits, I will explain how this method circumvent the need of a random permutation for security analysis of a generic QKD protocol. I will also present how a shield forged from error correction, can be used to improve the key rate of a generic QKD protocol. The shield is actually a system that does not contribute the key, but that is not under the eavesdropper's control. The latter argument is a generalization, from a different perspective, of an observation from Kraus, Branciard and Renner to improve the secret key generation rates of SARG04 by considering a different symmetrization. This is joint work with Joseph M. Renes.

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