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We describe a simple method to derive high performance semidefinite programming relaxations for optimizations over complex and real operator algebras in finite dimensional Hilbert spaces. The method is very flexible, easy to program and allows the user to assess the behavior of finite dimensional quantum systems in a number of interesting setups. We use this method to bound the strength of quantum nonlocality in bipartite and tripartite Bell scenarios where the dimension of a subset of the parties is bounded from above. We derive new results in quantum communication complexity and prove the soundness of the prepare-and-measure dimension witnesses introduced in [Phys. Rev. Lett. 105, 230501 (2010)]. Finally, we propose a new dimension witness that can distinguish between classical, real and complex two-level systems.
We present a method to certify the presence of Bell correlations in experimentally observed statistics, and to obtain new Bell inequalities. Our approach is based on relaxing the conditions defining the set of correlations obeying a local hidden vari
We construct a linear system non-local game which can be played perfectly using a limit of finite-dimensional quantum strategies, but which cannot be played perfectly on any finite-dimensional Hilbert space, or even with any tensor-product strategy.
Finite-size error (FSE), the discrepancy between an observable in a finite system and in the thermodynamic limit, is ubiquitous in numerical simulations of quantum many body systems. Although a rough estimate of these errors can be obtained from a se
We study and extend the semidefinite programming (SDP) hierarchies introduced in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical correlations arising from finite dimensional quantum systems. First, we introduce the dimensio
We introduce various measures of forward classical communication for bipartite quantum channels. Since a point-to-point channel is a special case of a bipartite channel, the measures reduce to measures of classical communication for point-to-point ch