# Towards Characterizing the Non-Locality of Entangled Quantum States

## Renato Renner and Stefan Wolf

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```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.