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Is genuine nonlocality in the triangle network exclusive to pure states?

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Abstract

Genuine network non-locality (GNN) refers to the existence of quantum correlations in a network with independent sources that cannot be explained by local hidden-variables (LHV) models. Even in the simplest scenario, determining whether these quantum correlations remain genuinely network non-local when derived from entangled states that deviate from their ideal forms is highly challenging due to the non-convex nature of local correlations. Understanding the boundary of these correlations thus becomes a hard problem, but one that raises academic interest specifically its robustness to noise. To address this problem, we introduce a causal domain-informed learning algorithm called the LHV k-rank neural network, which assesses the rank parameter of the non-ideal combined state produced by sources. Applied to the triangle network scenario with the three sources generating a class of quantum states known as X states, the neural network reveals that non-locality persists only if the states remain pure. Remarkably, we find that even slight deviations from ideal Bell states due to noise cause GNN to vanish, exhibiting a discrete behavior that hasn't been witnessed in the standard bell scenario. This finding thus raises a fundamental question as to whether GNN in the triangle network is exclusive to pure states or not. Additionally, we explore the case of the three sources producing dissimilar states, indicating that GNN requires all its sources to send pure entangled states with joint entangled measurements as resources. Apart from these results, this work succeeds in showing that machine learning approaches with domain-specific constraints can greatly benefit the field of quantum foundations.

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Classifying phases of matter is a central problem in physics. For quantum mechanical systems, this task can be daunting owing to the exponentially large Hilbert space. Thanks to the available computing power and access to ever larger data sets, classification problems are now routinely solved using machine learning techniques. Here, we propose to use a neural network based approach to find phase transitions depending on the performance of the neural network after training it with deliberately incorrectly labelled data. We demonstrate the success of this method on the topological phase transition in the Kitaev chain, the thermal phase transition in the classical Ising model, and the many-body-localization transition in a disordered quantum spin chain. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to a generic tool to identify unexplored phase transitions.
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More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in 'loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.
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The concept of bilocality was introduced to study the correlations which arise in an entanglement swapping scenario, where one has two sources which can naturally taken to be independent. This additional constraint leads to stricter requirements than simply imposing locality, in the form of bilocality inequalities. In this work we consider a natural generalisation of the bilocality scenario, namely the star-network consisting of a single central party surrounded by n edge parties, each of which shares an independent source with the centre. We derive new inequalities which are satisfied by all local correlations in this scenario, for the cases when the central party performs (i) two dichotomic measurements (ii) a single Bell state measurement. We demonstrate quantum violations of these inequalities and study both the robustness to noise and to losses.
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The correlations that can be observed between a set of variables depend on the causal structure underpinning them. Causal structures can be modeled using directed acyclic graphs, where nodes represent variables and edges denote functional dependencies. In this work, we describe a general algorithm for computing information-theoretic constraints on the correlations that can arise from a given interaction pattern, where we allow for classical as well as quantum variables. We apply the general technique to two relevant cases: First, we show that the principle of information causality appears naturally in our framework and go on to generalize and strengthen it. Second, we derive bounds on the correlations that can occur in a networked architecture, where a set of few-body quantum systems is distributed among a larger number of parties.
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