Quantum non-locality in two three-level systems

Nonlocality, manifested by the violation of Bell inequalities, indicates quantum entanglement in the underlying system. A natural question that arises is how much entanglement is required for a given nonlocal behavior. In this paper, we explore this question by quantifying entanglement using a family of generalized Clauser-Horne-Shimony-Holt-type Bell inequalities. We focus on two entanglement measures, entanglement of formation and one-way distillable entanglement, which are...

While all bipartite pure entangled states are known to generate correlations violating a Bell inequality, and are therefore nonlocal, the quantitative relation between pure-state entanglement and nonlocality is poorly understood. In fact, some Bell inequalities are maximally violated by non-maximally entangled states and this phenomenon is also observed for other operational measures of nonlocality. In this work, we study a recently proposed measure of nonlocality defined as ...

The structure of Bell-type inequalities detecting genuine multipartite non-locality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite non-locality in scenarios invol...

We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The resu...

In a multipartite setting, it is possible to distinguish quantum states that are genuinely $n$-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely $n$-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. T...

We identify the simplest combinations of entanglement and incompatibility giving the maximum quantum violation for each of the 46 classes of tight Bell inequalities for the (3,2,2) scenario, i.e., three parties, two measurements per party, and two outcomes per measurement. This allows us to classify the maximum quantum nonlocality according to the simplest resources needed to achieve it. We show that entanglement and incompatibility only produce maximum nonlocality when they ...

Understanding the quantitative relation between entanglement and Bell nonlocality is a longstanding open problem of both fundamental and practical interest. Here we provide a general approach to address this issue. Starting with an observation that entanglement measures, while defined dramatically different in mathematics, are basically the distances between the state of interest and its closest separable state, we relate this minimal distance between states with distance-bas...

Nonlocality is the most characteristic feature of quantum mechanics. John Bell, in his seminal 1964 work, proved that local-realism imposes a bound on the correlations among the measurement statistics of distant observers. Surpassing this bound rules out local-realistic description of microscopic phenomena, establishing the presence of nonlocal correlation. To manifest nonlocality, it requires, in the simplest scenario, two measurements performed randomly by each of two dista...

We study the relation between distillability of multipartite states and violation of Bell's inequality. We prove that there exist multipartite bound entangled states (i.e. non-separable, non-distillable states) that violate a multipartite Bell inequality. This implies that (i) violation of Bell's inequality is not a sufficient condition for distillability and (ii) some bound entangled states cannot be described by a local hidden variable model.

Quantum mechanics imposes limits on the values of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for simultaneous violation of multiple Bell inequalities. In the simplest case of three observers it has been shown that violation of one Bell inequality precludes any violation of other inequalities, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signalling principl...