Constraining the doability of relativistic quantum tasks

Abstract

We show within the framework of relativistic quantum tasks that the doability of any task is fully determined by a small subset of its parameters that we call its "coarse causal structure", as well as the distributed computation it aims to accomplish. We do this by making rigorous the notion of a protocol using a structure known as a spacetime circuit, which describes how a computation is preformed across a region of spacetime. Using spacetime circuits we show that any protocol that can accomplish a given task can, without changing its doability, undergo significant geometric modifications such as changing the background spacetime and moving the location of input and output points, so long as the coarse causal structure of the task is maintained. Besides giving a powerful tool for determining the doability of a task, our results strengthen the no-go theorem for position based quantum cryptography to include arbitrary sending and receiving of signals by verifier agents outside the authentication region. They also serve as a consistency check for the holographic principle by showing that discrepancies between bulk and boundary causal structure can not cause a task to be doable in one but not the other.