Bounding and Simulating Contextual Correlations in Quantum Theory

We introduce a hierarchy of semidefinite relaxations the set quantum correlations in generalised contextuality scenarios. This constitutes simple and versatile tool for bounding magnitude contextuality. To illustrate its utility, we use it to determine maximal violation several noncontextuality inequalities whose maximum violations were previously unknown. then go further prove that certain preparation-contextual cannot be explained with pure states, thereby showing mixed states are an indispensable resource In second part paper, turn our attention simulation general operational theories. information cost simulating preparation contextuality, which quantifies additional, otherwise forbidden, required simulate contextual either classical or models. both cases, show can efficiently bounded using variant relaxations, calculate exactly simplest scenario parity-oblivious multiplexing.