Classification of no-signaling correlation and the “guess your neighbor's input” game

We formulate a series of nontrivial equalities which are satisfied by all no-signaling correlations, meaning that no faster-than-light communication is allowed with the resource of these correlations. All quantum and classical correlations satisfy these equalities since they are no-signaling. By applying these equalities, we provide a general framework for solving the multipartite “guess your neighbor's input” (GYNI) game, which is naturally no-signaling but shows conversely that general no-signaling correlations are actually more nonlocal than those allowed by quantum mechanics. We confirm the validity of our method for the number of players from 3 up to 19, thus providing convincing evidence that it works for the general case. In addition, we solve analytically the tripartite GYNI and obtain a computable measure of supraquantum correlations. This result simplifies the defined optimization procedure to an analytic formula, thus characterizing explicitly the boundary between quantum and supraquantum correlations. In addition, we show that the gap between quantum and no-signaling boundaries containing supraquantum correlations can be closed by local orthogonality conditions in the tripartite case. Our results provide a computable classification of no-signaling correlations.

Figure 1

The game of “guess your neighbor's input” [27]. The aim is that each player provides an output bit $a_i\in \{0,1\}$ representing the guess about his or her right-hand neighbor's input. Here $\{0,1\}$ are represented by “spade” and “heart” on the cards. No communication is allowed after the inputs are distributed in this game.

Figure 2

Winning probability ratio for no-signaling correlations over classical or quantum correlations. We assume $N$ is odd. The star symbols represent our result of Eq. (1), which will approach 2 asymptotically when $N$ is large.

Figure 3

Schematic representation of various correlations, including classical, quantum, and no-signaling correlations. The Bell equality and the GYNI game can identify different boundaries between those correlations. The well-known Bell inequality is also marked.

Figure 4

Geometric representation of no-signaling inequalities for the tripartite case. Cases for larger $N$ can also be represented in a similar way. Two classes of inequalities corresponding to the left and right panels are presented.