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Abstract

In this Letter we show that quantum nonlocality can be superactivated. That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself. In the second part of this work we study how large these violations can be. In particular, we show the existence of quantum states with very low Bell violation but such that five copies of them give very large violations. In fact, this gap can be made arbitrarily large by increasing the dimension of the states. DOI: 10.1103/PhysRevLett.109.190401 PACS numbers: 03.65.Ud, 03.65.Ta, 03.67.Mn The fact that by combining two quantum objects one can get something better than the sum of their individual uses seems to be a characteristic feature of quantum mechanics. In particular, in quantum information theory this effect has been extensively studied in quantum channel theory (see, for instance, [1][2][3]) and entanglement theory (see, for instance, [4,5]). Actually, some of these works show a much stronger behavior called superactivation. That is, one can get a quantum effect by combining two objects with no quantum effects. The aim of this work is to study this phenomenon in the context of quantum nonlocality.The study of quantum nonlocality dates back to the seminal work by Bell [6]. In this work the author took the apparently metaphysical dispute arising from the previous intuition of Einstein, Podolsky, and Rosen [7] and formulated it in terms of assumptions which naturally lead to a refutable prediction. Given two spatially separated quantum systems, controlled by Alice and Bob, respectively, and specified by a bipartite quantum state , Bell showed that certain probability distributions pða; bjx; yÞ obtained from an experiment in which Alice and Bob perform some measurements x and y in their corresponding systems with possible outputs a and b, respectively, cannot be explained by a local hidden variable model (LHVM). Specifically, Bell showed that the assumption of a LHVM implies some inequalities on the set of probability distributions pða; bjx; yÞ, since then called Bell inequalities, which are violated by certain quantum probability distributions produced with an entangled state.Though initially discovered in the context of foundations of quantum mechanics, violations of Bell inequalities, commonly known as quantum nonlocality, are nowadays a key point in a wide range of branches of quantum information science. In particular, nonlocal probability distributions provide the quantum advantage in the security of quantum cryptography protocols [8,9], in communication complexity protocols (see the recent review [10]), and in the generation of trusted random numbers [11].In order to pass from the probability distribution level to the quantum state level, we say that a bipartite quantum state is nonlocal if it can lead to certain quantum probability distributions pða; bjx; yÞ in an Alice-Bob scenario violating some Bell inequality. In the case where any probability distribution pða; bjx; yÞ produced with the state can be explained by a LHVM, we say ...