Structure of Quantum Theory

Given a collection of quantum states in one lab, how costly is it to send them to another lab by using only classical communication resources? We introduce a framework for assessing the classical cost of sending quantum states and explore its consequences. The main focus of the talk is on two highlights of the ensuing analysis. First, we determine the scaling of the classical complexity needed to account for all quantum states. This gives insight to the fundamental advantage of quantum resources. Second, we prove that the proposed notion of classical communication is necessary and sufficient for quantum correlation advantages in a three-party prepare-and-measure-like scenario. This gives it a clear task-interpretation to our concept. As a corollary, it follows that the cost of classically simulating the correlations obtained from quantum states diverges (with known scaling), even for qubits where limitation to the standard prepare-and-measure scenario allows classical simulation with just two bits. This suggests that, in analogy with the traditional Bell experiments versus more sophisticated nonlocality tests, the historical focus on the simplest scenario (namely the prepare-and-measure scenario) has artificially hidden the full power of the quantum correlations that can be generated from quantum states.