Failure of the trilinear operator space Grothendieck theorem

We give a counterexample to a trilinear version of the operator space Grothendieck theorem. In particular, we show that for trilinear forms on $\ell_\infty$, the ratio of the symmetrized completely bounded norm and the jointly completely bounded norm is in general unbounded, answering a question of Pisier. The proof is based on a non-commutative version of the generalized von Neumann inequality from additive combinatorics.Comment: Reformatted for Discrete Analysi

Large bipartite Bell violations with dichotomic measurements

In this paper we introduce a simple and natural bipartite Bell scenario, by considering the correlations between two parties defined by general measurements in one party and dichotomic ones in the other. We show that unbounded Bell violations can be obtained in this context. Since such violations cannot occur when both parties use dichotomic measurements, our setting can be considered as the simplest one where this phenomenon can be observed. Our example is essentially optimal in terms of the outputs and the Hilbert space dimension

Labor productivity: a comparative analysis of the European Union and United States, for the period 1994-2007

This Working Ppaer confirms that labor productivity in the European economies has continued to slow down in recent years. U.S. productivity growth has been higher than in the EU, but only since 2001. At the same time, both economies have modified previous employment performance: EU employment growth is now higher than in U.S. This article proposes that productivity growth be explained by demand dynamics, and investment in particular, not forgetting the influence of employment, along with other factors such as new technologies.Labor Productivity; Demand; Employment; Labor Markets; Economic Sectors

Quantum Query Algorithms are Completely Bounded Forms

We prove a characterization of $t$-query quantum algorithms in terms of the unit ball of a space of degree-$2t$ polynomials. Based on this, we obtain a refined notion of approximate polynomial degree that equals the quantum query complexity, answering a question of Aaronson et al. (CCC'16). Our proof is based on a fundamental result of Christensen and Sinclair (J. Funct. Anal., 1987) that generalizes the well-known Stinespring representation for quantum channels to multilinear forms. Using our characterization, we show that many polynomials of degree four are far from those coming from two-query quantum algorithms. We also give a simple and short proof of one of the results of Aaronson et al. showing an equivalence between one-query quantum algorithms and bounded quadratic polynomials.Comment: 24 pages, 3 figures. v2: 27 pages, minor changes in response to referee comment

Reducing the number of inputs in nonlocal games

In this work we show how a vector-valued version of Schechtman's empirical method can be used to reduce the number of inputs in a nonlocal game $G$ while preserving the quotient $\beta^*(G)/\beta(G)$ of the quantum over the classical bias. We apply our method to the Khot-Vishnoi game, with exponentially many questions per player, to produce another game with polynomially many ($N\approx n^8$) questions so that the quantum over the classical bias is $\Omega (n/\log^2 n)$