With the goal of gaining a deeper understanding of quantum non-locality, we decompose quantum correlations into more elementary non-local correlations. We show that the correlations of all pure entangled states of two qubits can be simulated without
communication, hence using only non-signaling resources. Our simulation model works in two steps. First, we decompose the quantum correlations into a local and a non-local part. Second, we present a model for simulating the nonlocal part using only non-signaling resources. In our model partially entangled states require more nonlocal resources than maximally entangled states, but the less the state is entangled, the less frequently must the nonlocal resources be used.
Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describes such correlations? We introduce the concept of dimension witness to put lower boun
ds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and Quantum Information applications.
