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oai:docta.ucm.es:20.500.14352/336952023-08-28T06:51:18Zcom_20.500.14352_14col_20.500.14352_15

On the largest Bell violation attainable by a quantum state Palazuelos Cabezón, Carlos 517 Quantum information theory Bell inequalities Projective tensor norm Hilbertian subspaces Análisis matemático 1202 Análisis y Análisis Funcional We study the projective tensor norm as a measure of the largest Bell violation of a quantum state. In order to do this, we consider a truncated version of a well-known SDP relaxation for the quantum value of a two-prover one-round game, one which has extra restrictions on the dimension of the SDP solutions. Our main result provides a quite accurate upper bound for the distance between the classical value of a Bell inequality and the corresponding value of the relaxation. Along the way, we give a simple proof that the best complementation constant of l(2)(n) in l(1) (l(infinity)) is of order root ln n As a direct consequence, we show that we cannot remove a logarithmic factor when we are computing the largest Bell violation attainable by the maximally entangled state. Unión Europea. FP7 Comunidad de Madrid MINECO: ICMAT Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-19T13:26:22Z 2023-06-19T13:26:22Z 2014-10-01 journal article https://hdl.handle.net/20.500.14352/33695 XXXX-XXXX 10.1016/j.jfa.2014.07.028 eng QUEVADIS (233859) QUITEMAD (S2009/ESP-1594) (MTM2011-26912) Severo Ochoa project (SEV-2011-0087) open access application/pdf Elsevier