A complete set of multidimensional Bell inequalities
نویسنده
چکیده
We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf in [31], and by Ẑukowski and Brukner in [32], for the two-dimensional case. Our construction applies for the n parties, two-observables case, where each observable is d-valued. The d n inequalities obtained involve homogeneous polynomials. They define the facets of a polytope in a complex vector space of dimension d. We detail the inequalities obtained in the case d = 3 and, from them, we recover known inequalities. We finally explain how the violations of our inequalities by Quantum Mechanics can be computed and could be observed, when using unitary observables.
منابع مشابه
Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth.
We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-Wolf-Żukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequa...
متن کاملBell inequalities with auxiliary communication.
What is the communication cost of simulating the correlations produced by quantum theory? We generalize Bell inequalities to the setting of local realistic theories augmented by a fixed amount of classical communication. Suppose two parties choose one of M two-outcome measurements and exchange 1 bit of information. We present the complete set of inequalities for M=2, and the complete set of ine...
متن کاملAsymptotic violation of Bell inequalities and distillability.
A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In th...
متن کاملfür Mathematik in den Naturwissenschaften Leipzig Gisin ’ s Theorem for Arbitrary Dimensional Multipartite States
We present a set of Bell inequalities which are sufficient and necessary for separability of general pure multipartite quantum states in arbitrary dimensions. The relations between Bell inequalities and distillability are also studied. We show that any quantum states that violate one of these Bell inequalities are distillable.
متن کامل