Quantum non-locality in two three-level systems

We explore the challenges posed by the violation of Bell-like inequalities by $d$-dimensional systems exposed to imperfect state-preparation and measurement settings. We address, in particular, the limit of high-dimensional systems, naturally arising when exploring the quantum-to-classical transition. We show that, although suitable Bell inequalities can be violated, in principle, for any dimension of given subsystems, it is in practice increasingly challenging to detect such...

It remains an open question whether every pure multipartite state that is genuinely entangled is also genuinely nonlocal. Recently, a new general construction of Bell inequalities allowing the detection of genuine multipartite nonlocality (GMNL) in quantum states was proposed in [F. J. Curchod, M. L. Almeida, and A. Acin, New J. Phys. 21, 023016 (2019) with the aim of addressing the above problem. Here we show how, in a simple manner, one can improve this construction to deli...

We propose a generalized Bell inequality for two three-dimensional systems with three settings in each local measurement. It is shown that this inequality is maximally violated if local measurements are configured to be mutually unbiased and a composite state is maximally entangled. This feature is similar to Clauser-Horne-Shimony-Holt inequality for two qubits but is in contrast with the two types of inequalities, Collins-Gisin-Linden-Massar-Popescu and Son-Lee-Kim, for high...

A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. The latter has however some drawbacks. First and foremost it is unfeasible to determine the whole set of Bell inequalities already for a few measurements and thus unfeasible to find the experimental setup maximizing their violation. Second, the Bell violation suffers from an a...

We present a family of Bell inequalities involving only two measurement settings of each party for N>2 qubits. Our inequalities include all the standard ones with fewer than N qubits and thus gives a natural generalization. It is shown that all the Greenberger-Horne-Zeilinger states violate the inequalities maximally, with an amount that grows exponentially as 2^{{(N-2)}/2}. The inequalities are also violated by some states that do satisfy all the standard Bell inequalities. ...

We provide an explicit example of a Bell inequality with 3 settings and 2 outcomes per site for which the largest violation is not obtained by the maximally entangled state, even if its dimension is allowed to be arbitrarily large. This complements recent results by Junge and Palazuelos (arXiv:1007.3042) who show, employing tools from operator space theory, that such inequalities do exist. Our elementary example provides arguably the simplest setting in which it can be demons...

The unique entanglement measure is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the non-locality. For justification, we extend the study to three qubits. We consider all possible 3-qubit operators with a symmetric permutation. When only considering one entanglement measure, the numerical result contradicts expectation. Therefor...

To date, most efforts to demonstrate quantum nonlocality have concentrated on systems of two (or very few) particles. It is however difficult in many experiments to address individual particles, making it hard to highlight the presence of nonlocality. We show how a natural setup with no access to individual particles allows one to violate the CHSH inequality with many pairs, including in our analysis effects of noise and losses. We discuss the case of distinguishable and indi...

Quantum theory allows for correlations between the outcomes of distant measurements that are inconsistent with any locally causal theory, as demonstrated by the violation of a Bell inequality. Typical demonstrations of these correlations require careful alignment between the measurements, which requires distant parties to share a reference frame. Here, we prove, following a numerical observation by Shadbolt et al., that if two parties share a Bell state and each party randoml...

To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average communication needed to produce these correlations. Moreover, for every probability distribution there exists an optimal inequality for which the degree of violation gives the minimal average communication. As an example, to produce using classic...