De Finetti Theorems for Quantum Conditional Probability Distributions with Symmetry

Abstract The aim of device-independent quantum key distribution (DIQKD) is to study protocols that allow the generation a secret shared between two parties under minimal assumptions on devices produce key. These are merely modeled as black boxes and mathematically described conditional probability distributions. A major obstacle in analysis DIQKD huge space possible box behaviors. De Finetti theorems can help overcome this problem by reducing have an iid structure. Here we show new de relate distributions set (convex combinations distributions) themselves set. We also how one these be used enforce some restrictions onto attacker protocol. Finally observe desirable strengthenings restriction, for instance collective attacks only, not straightforwardly possible.