Quantum Computation and Information Seminar 

06/02/2019, 11:00 — 12:00 — Room P3.10, Mathematics Building
João Ribeiro, Imperial College London

Information-theoretic key agreement and classical bound entanglement

Suppose Alice and Bob want to agree on a shared key which they want to keep secret from Eve, who can eavesdrop on their communication and has unlimited computational power. Towards this goal, we assume that all parties have access to correlated randomness. This is the setting of (classical) information-theoretic key agreement, which has been notoriously difficult to understand.

I will start by presenting some seminal results in this area. Then, I will briefly discuss a recent work where we characterize the asymptotic behavior of the secret-key rate (which measures how efficiently Alice and Bob can create shared secret bits) in an alternative setting where the honest parties can optimize the distribution of correlated randomness under some constraint. In contrast, even approximating the secret-key rate in the original setting with non-trivial correlated randomness appears to be a very hard problem.

In the second part, I will focus on a conjecture with strong ties to the concept of bound entanglement from quantum information theory.

Namely, the conjecture asks whether “bound information” exists: Are there distributions of correlated randomness that “contain” secret bits which cannot be extracted via a key agreement protocol? In particular, it is believed that bound entangled quantum states lead to such classical distributions. To conclude, I will discuss how NOT to show bound information exists.

(Partially based on joint work with Daniel Jost and Ueli Maurer, ETH Zurich)