[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125018-en":3,"doc-seo-125018-105":30,"detail-sidebar-cat-0-en-105":95},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125018,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Machine learning meets the CHSH scenario","This work studies machine learning methods for characterising the quantum set of correlations, focusing on the CHSH scenario in both its 4-dimensional case (with a known analytical solution) and 8-dimensional case (without one). It evaluates a broad range of models from basic data science approaches to dense neural networks, highlighting support vector machines and dense neural networks as the strongest performers. While average performance is easy to achieve, “hard” boundary cases are difficult, especially for 8 dimensions, requiring carefully tailored training data. The study stresses the risk of bias introduced by implicit data selection criteria.","arXiv :2407 . 14396v1 [ quant-ph] 19 Jul 2024  \nMachine learning meets the CHSH scenario  \nGabriel Pereira Alves 1 ,∗ Nicolas Gigena2 ,† and Jędrzej Kaniewski 1‡  \n1 Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland and  \n2 IFLP/CONICET and Departamento de Física, Universidad Nacional de La Plata, C. C. 67, La Plata (1900), Argentina.(Dated: July 22, 2024)  \nIn this work, we perform a comprehensive study of the machine learning (ML) methods for the purpose of characterising the quantum set of correlations. As our main focus is on assessing the usefulness and effectiveness of the ML approach, we focus exclusively on the CHSH scenario, both the 4-dimensional variant, for which an analytical solution is known, and the 8-dimensional variant, for which no analytical solution is known, but numerical approaches are relatively well understood. We consider a wide selection of approaches, ranging from simple data science models to dense neural networks. The two classes of models that perform well are support vector machines and dense neural networks, and they are the main focus of this work. We conclude that while it is relatively easy to achieve good performance on average, it is hard to train a model that performs well on the \"hard\"cases, i.e., points in the vicinity of the boundary of the quantum set. Sadly, these are precisely the cases which are interesting from the academic point of view. In order to improve performance on hard cases one must, especially for the 8-dimensional problem, resort to a tailored choice of training data, which means that we are implicitly feeding our intuition and biases into the model. We feel that this is an important and often overlooked aspect of applying ML models to academic problems, where data generation or data selection is performed according to some implicit subjective criteria. In this way, it is possible to unconsciously steer our model, so that it exhibits features that we are interested in seeing. Hence, special care must be taken while determining whether ML methods can be considered objective and unbiased in the context of academic problems.  \nI. INTRODUCTION  \nProposed in 1964 [1], Bell non-locality [2] establishes that the predictions of quantum mechanics are inconsistent with local hidden-variables (LHV) models, constituting a fundamental aspect of quantum correlations in spatially separated systems. The so-called Clauser-HorneShimony-Holt (CHSH) scenario [3] is the simplest scenario in which the correlations observed by two parties can be verified as not admitting a local-realistic explanation, assuming that the shared quantum state is entangled and that the pair of dichotomic measurements implemented by each party is incompatible [4] . Such correlations are identifiable through the violation of Bell inequalities, and assessing the extent of these violations has always been a question of broad interest. Tsirelson was one of the first to look into the topic, deriving, in 1980 [5], an upper bound for the violation of the CHSHinequality, a limit that would later come to be known as Tsirelson’s bound. In the same direction, Tsirelson himself, in 1987 [6], followed by others [7–9], obtained a tighter characterisation in the form of a nonlinear inequality restricting the set of quantum correlations, currently known as the TLM inequality. The latter, even if satisfied by any quantum correlation, is sufficient only when the local outcomes of Alice and Bob have uniform distributions.  \nExploiting the fact that the set of quantum correlations is convex, two complementary heuristic approaches  \n∗  \n†  \n‡  \n[gpereira@fuw.edu.pl](gpereira@fuw.edu.pl)[ ](gpereira@fuw.edu.pl)[nicolas.gigena@fisica.unlp.edu.ar](nicolas.gigena@fisica.unlp.edu.ar)[jkaniewski@fuw.edu.pl](jkaniewski@fuw.edu.pl)  \nare often used to find maximum values of a given Bell inequality. On the one hand, outer approximations to the quantum set can be obtained through the NPA hierarchy [10] of semi-definit","cbCaigwuEjQYB5md","https://ap.wps.com/l/cbCaigwuEjQYB5md","pdf",15198020,1,15,"English","en",105,"# Introduction\n## Bell non-locality and the CHSH scenario\n## Quantum bounds and characterisations\n## NPA hierarchy and see-saw optimisation\n## Motivation for ML in quantum information\n## Goals and focus of the study","[{\"question\":\"Which CHSH settings does the study consider, and why?\",\"answer\":\"It examines both the 4-dimensional variant, where an analytical solution exists, and the 8-dimensional variant, where no analytical solution is known but numerical methods are understood.\"},{\"question\":\"Which machine learning model families perform best?\",\"answer\":\"Support vector machines and dense neural networks are identified as the two model classes that perform well and receive primary attention.\"},{\"question\":\"What challenge arises when predicting “hard” quantum boundary cases?\",\"answer\":\"Achieving good performance on hard cases near the boundary of the quantum set is difficult, even though average performance is relatively easy.\"},{\"question\":\"How can training data choices affect outcomes and potential bias?\",\"answer\":\"Especially in the 8-dimensional problem, improving hard-case performance requires tailored training data, which implicitly injects intuition and biases into the model, raising concerns about objectivity and unbiased learning in academic contexts.\"}]","Machine learning meets the CHSH scenario | 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CHSH settings does the study consider, and why?","Question",{"text":75,"@type":76},"It examines both the 4-dimensional variant, where an analytical solution exists, and the 8-dimensional variant, where no analytical solution is known but numerical methods are understood.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Which machine learning model families perform best?",{"text":80,"@type":76},"Support vector machines and dense neural networks are identified as the two model classes that perform well and receive primary attention.",{"name":82,"@type":73,"acceptedAnswer":83},"What challenge arises when predicting “hard” quantum boundary cases?",{"text":84,"@type":76},"Achieving good performance on hard cases near the boundary of the quantum set is difficult, even though average performance is relatively easy.",{"name":86,"@type":73,"acceptedAnswer":87},"How can training data choices affect outcomes and potential bias?",{"text":88,"@type":76},"Especially in the 8-dimensional 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