Towards Characterizing the Non-Locality of Entangled Quantum States
Renato Renner and Stefan Wolf
The behavior of entangled quantum systems can generally not be explained as being determined by shared classical randomness. In the first part of this paper, we propose a simple game for $n$ players demonstrating this non-local property of quantum mechanics: While, on the one hand, it is immediately clear that classical players will lose the game with substantial probability, it can, on the other hand, always be won by players sharing an entangled quantum state. The simplicity of the classical analysis of our game contrasts the often quite involved analysis of previously proposed examples of this type. In the second part, aiming at a quantitative characterization of the non-locality of $n$-partite quantum states, we consider a general class of $n$-player games, where the amount of communication between certain (randomly chosen) groups of players is measured. Comparing the classical communication needed for both classical players and quantum players (initially sharing a given quantum state) to win such a game, a new type of separation results is obtained. In particular, we show that in order to simulate two separated qubits of an $n$-partite GHZ state at least $\Omega(\log \log n)$ bits of information are required.