Local orthogonality as a multipartite principle for quantum correlations

Abstract

In recent years, the use of information principles to understand quantum correlations has been very successful. Unfortunately, all principles considered so far have a bipartite formulation, but intrinsically multipartite principles, yet to be discovered, are necessary for reproducing quantum correlations. Here we introduce local orthogonality, an intrinsically multipartite principle stating that events involving different outcomes of the same local measurement must be exclusive or orthogonal. We prove that it is equivalent to no-signalling in the bipartite scenario but more restrictive for more than two parties. By exploiting this nonequivalence, it is then demonstrated that some bipartite supra-quantum correlations do violate the local orthogonality when distributed among several parties. Finally, we show how its multipartite character allows revealing the non-quantumness of correlations for which any bipartite principle fails. We believe that local orthogonality is a crucial ingredient for understanding no-signalling and quantum correlations.

Exclusivity principle forbids sets of correlations larger than the quantum set

“…While previous principles cannot rule out the existence of sets of correlations strictly larger than the quantum one for any single experiment [6][7][8][9][10][11][12][13][14], we have shown that, for self-complementary graphs, the E principle, by itself, excludes any set of correlations strictly larger than the quantum set.…”

“…In addition, when applied to the OR product of an infinite number of copies, there is strong evidence that the E principle singles out the maximum quantum violation of the NC inequalities whose exclusivity graph is the complement of odd cycles on n ≥ 7 vertices [22]. Indeed, it might be also the case that, when applied to an infinite number of copies, the E principle singles out the Tsirelson bound of the CHSH inequality [14,20].…”

“…[33] it was shown that, when we consider the experiment to test S w alone, then the maximum value of S w allowed by the E principle is given by the weighted version of the fractional packing of G, α * (G, w) [38]. The principle of local orthogonality [14] may be seen as the E principle restricted to Bell scenarios. However, when this restriction is removed is when the E principle shows itself more powerful, since while for a given graph G, there is always a NC inequality for which QT reaches ϑ (G) [33], this is not true if "NC inequality" is replaced by "Bell inequality" [21].…”

“…When applied to the OR product of two copies of the exclusivity graph (which may be seen as two copies of the same experiment), the E principle singles out the maximum quantum value for experiments whose exclusivity graphs are vertex-transitive and self-complementary [20], which include the simplest NC inequality violated by QT, namely the Klyachko-CanBinicioglu-Shumovsky (KCBS) inequality [18]. Moreover, either applied to two copies of the exclusivity graph of the Clauser-Horne-Shimony-Holt (CHSH) [39] Bell inequality [14] or of a simpler inequality [20], the E principle excludes Popescu-Rohrlich nonlocal boxes [6] and provides an upper bound to the maximum violation of the CHSH inequality which is close to the Tsirelson bound [40]. In addition, when applied to the OR product of an infinite number of copies, there is strong evidence that the E principle singles out the maximum quantum violation of the NC inequalities whose exclusivity graph is the complement of odd cycles on n ≥ 7 vertices [22].…”

“…One consists of reconstructing QT as a purely operational probabilistic theory that follows from some sets of axioms [1][2][3][4][5]. A second approach consists of identifying principles that explain the set of quantum nonlocal correlations [6][7][8][9][10][11][12][13][14]. The third approach consists of identifying principles that explain the set of quantum contextual correlations [15][16][17][18][19] without restrictions imposed by a specific experimental scenario [20][21][22][23].…”