Quantum Information

We investigate weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating player can try to bias the output bit towards a preferred value. A weak coin-flipping protocol has a bias ϵ if neither player can force the outcome towards their preferred value with probability more than 1/2+ϵ. While it is known that classically ϵ=1/2, Mochon showed in 2007 [arXiv:0711.4114] that quantumly weak coin flipping can be achieved with arbitrarily small bias, i.e. ϵ(k)=1/(4k+2) for arbitrarily large k, and he proposed an explicit protocol approaching bias 1/6. So far, the best known explicit protocol is the one by Arora, Roland and Weis, with ϵ(2)=1/10 (corresponding to k=2) [STOC'19, p. 205-216]. In the current work, we present the construction of protocols approaching arbitrarily close to zero bias, i.e. ϵ(k) for arbitrarily large k. We connect the algebraic properties of Mochon's assignments---at the heart of his proof of existence---with the geometric properties of the unitaries whose existence he proved. It is this connection that allows us to find these unitaries analytically.

The approach to quantum theory known as QBism notoriously asserts that the quantum state is not even a partial representation of reality, but instead quantifies an agent's subjective degrees of belief about future experiences. Despite its counter-intuitive premise, QBists argue that this interpretation has the potential to illuminate and demystify certain aspects of quantum theory. In this talk I will discuss how `causality' might be interpreted by a QBist, and whether doing so might help us understand the bizarre hypothetical phenomenon of `indefinite causality'.

The possibility of indefinite causal order has garnered considerable interest in recent years, both for its promise as a resource, e.g. for communication, and for its role in exploring the fundamental physical constraints on causal structure. In order to gain a better understanding of the phenomenon, one approach is to design experiments that implement – or at least simulate – scenarios with indefinite causal order. While post-selection is one way to simulate exotic causal structures, this approach may not provide the desired insights. Instead, I will discuss how one might go about implementing indefinite causal order without post-selection.