Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0009
V. Scarani
The behaviors that obey the no-signaling condition are a natural set to study nonlocality: this chapter is devoted to it. First, the most famous example of a no-signaling non-quantum behavior is introduced, the so-called Popescu-Rohrlich (PR) box. Then, some “typical quantum” features are recovered in the no-signaling framework, showing that they are common to all no-signaling theories.
{"title":"Nonlocality in the No-Signaling Framework","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0009","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0009","url":null,"abstract":"The behaviors that obey the no-signaling condition are a natural set to study nonlocality: this chapter is devoted to it. First, the most famous example of a no-signaling non-quantum behavior is introduced, the so-called Popescu-Rohrlich (PR) box. Then, some “typical quantum” features are recovered in the no-signaling framework, showing that they are common to all no-signaling theories.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123127477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0008
V. Scarani
Nonlocality certifies that the outputs of a measurement did not pre-exist, which in particular means that they were unpredictable or random. In other words, nonlocality certifies randomness in a device-independent way. This chapter introduces the main tools for the study and quantification of randomness: process randomness, the need for a predictor or adversary, and guessing probability. Examples are then explicitly worked out, and a review of more advanced results is provided.
{"title":"Certifying Randomness","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0008","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0008","url":null,"abstract":"Nonlocality certifies that the outputs of a measurement did not pre-exist, which in particular means that they were unpredictable or random. In other words, nonlocality certifies randomness in a device-independent way. This chapter introduces the main tools for the study and quantification of randomness: process randomness, the need for a predictor or adversary, and guessing probability. Examples are then explicitly worked out, and a review of more advanced results is provided.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122843812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0001
V. Scarani
This chapter is a self-contained introduction to Bell nonlocality. After a very quick historical motivation, the setting and the definition of nonlocality are given. Five classic examples of Bell tests are then introduced, including the CHSH and the GHZ tests. The remainder of the chapter is a critical reflection that contains two topics: a discussion of possible loopholes that should be avoided, and an elementary presentation of the main interpretations given to the phenomenon of nonlocality.
{"title":"First Encounter with Bell Nonlocality","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0001","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0001","url":null,"abstract":"This chapter is a self-contained introduction to Bell nonlocality. After a very quick historical motivation, the setting and the definition of nonlocality are given. Five classic examples of Bell tests are then introduced, including the CHSH and the GHZ tests. The remainder of the chapter is a critical reflection that contains two topics: a discussion of possible loopholes that should be avoided, and an elementary presentation of the main interpretations given to the phenomenon of nonlocality.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127263840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0007
V. Scarani
This chapter is devoted to deviice-independent self-testing. This refers to the fact that some extremal behaviors in the quantum set can actually be realised only with specific measurements on a specific shared entangled state. The two main examples, namely the maximal value of CHSH and the Mayers-Yao test, are described in detail before the abstract definition of self-testing is given.
{"title":"Device-Independent Self-Testing","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0007","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0007","url":null,"abstract":"This chapter is devoted to deviice-independent self-testing. This refers to the fact that some extremal behaviors in the quantum set can actually be realised only with specific measurements on a specific shared entangled state. The two main examples, namely the maximal value of CHSH and the Mayers-Yao test, are described in detail before the abstract definition of self-testing is given.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115743575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0005
V. Scarani
This chapter discusses nonlocality for scenarios with more than two players. The definition of locality is the obvious generalisation of the bipartite case, but now there are many more ways in which locality can be violated. First, the main families of inequalities are presented. Then, the definition and demonstration of genuine multipartite nonlocality is discussed.
{"title":"Multipartite Bell Nonlocality","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0005","url":null,"abstract":"This chapter discusses nonlocality for scenarios with more than two players. The definition of locality is the obvious generalisation of the bipartite case, but now there are many more ways in which locality can be violated. First, the main families of inequalities are presented. Then, the definition and demonstration of genuine multipartite nonlocality is discussed.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131558361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0006
V. Scarani
Part II is devoted to the applied side of nonlocality: device-independent certification of quantumness. After an introduction to this idea, the first chapter deals with the characterisation of the set of quantum behaviors. Since this set is not easily parametrised, in practice one often works with outer approximations, membership of which can be cast as a semi-definite program.
{"title":"The Set of Quantum Behaviors","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0006","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0006","url":null,"abstract":"Part II is devoted to the applied side of nonlocality: device-independent certification of quantumness. After an introduction to this idea, the first chapter deals with the characterisation of the set of quantum behaviors. Since this set is not easily parametrised, in practice one often works with outer approximations, membership of which can be cast as a semi-definite program.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124097844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0011
V. Scarani
This last chapter studies the relaxation of the conditions of no-signaling and measurement independence. For signaling models, after stressing the need for fine-tuning, it is shown that the speed of the hypothetical influence cannot be finite. For measurement dependence, the tolerable amount is discussed, and the related notion of randomness amplification is introduced.
{"title":"Signaling and Measurement Dependence","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0011","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0011","url":null,"abstract":"This last chapter studies the relaxation of the conditions of no-signaling and measurement independence. For signaling models, after stressing the need for fine-tuning, it is shown that the speed of the hypothetical influence cannot be finite. For measurement dependence, the tolerable amount is discussed, and the related notion of randomness amplification is introduced.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114999086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0012
V. Scarani
We first stress that nonlocality forces changes on our view of the world. One can adopt the orthodox view that one should not even attempt to describe individual events; or one can opt for a properly-speaking nonlocal model, with very unpleasant features like influences propagating at infinite speed in our space-time; or one can go all the way to some form of determinism. Then, the hope is formulated that the field of nonlocality, having reached maturity, may serve as starting point for future discoveries.
{"title":"Epilogue","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0012","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0012","url":null,"abstract":"We first stress that nonlocality forces changes on our view of the world. One can adopt the orthodox view that one should not even attempt to describe individual events; or one can opt for a properly-speaking nonlocal model, with very unpleasant features like influences propagating at infinite speed in our space-time; or one can go all the way to some form of determinism.\u0000Then, the hope is formulated that the field of nonlocality, having reached maturity, may serve as starting point for future discoveries.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126211049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0010
V. Scarani
The fact that the no-signaling set is larger than the quantum set suggests that the excess regions could be cut off by invoking additional constraints. In this chapter, we present some of the constraints that have been proposed as “physical principles”: information causality, macroscopic locality and local orthogonality. All three capture interesting features of the quantum set but fail to single ti out exactly.
{"title":"The Quest for Device-Independent Quantum Principles","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0010","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0010","url":null,"abstract":"The fact that the no-signaling set is larger than the quantum set suggests that the excess regions could be cut off by invoking additional constraints. In this chapter, we present some of the constraints that have been proposed as “physical principles”: information causality, macroscopic locality and local orthogonality. All three capture interesting features of the quantum set but fail to single ti out exactly.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116786341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-07DOI: 10.1093/oso/9780198788416.003.0002
V. Scarani
This chapter covers the essential mathematical tools for the study of nonlocality. It begins with the main object under study: a collection of several probability distributions usually called “behavior”. The crucial definition of locality is then given, followed by Fine’s theorem that relates local behaviors to pre-existing values and clarifies the role of local deterministic processes. In turn, one finds that local behaviors belong to a polytope, whose facets are Bell inequalities. The simplest scenario, called CHSH, is studied in detail.
{"title":"Formalizing Bell Nonlocality","authors":"V. Scarani","doi":"10.1093/oso/9780198788416.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198788416.003.0002","url":null,"abstract":"This chapter covers the essential mathematical tools for the study of nonlocality. It begins with the main object under study: a collection of several probability distributions usually called “behavior”. The crucial definition of locality is then given, followed by Fine’s theorem that relates local behaviors to pre-existing values and clarifies the role of local deterministic processes. In turn, one finds that local behaviors belong to a polytope, whose facets are Bell inequalities. The simplest scenario, called CHSH, is studied in detail.","PeriodicalId":135183,"journal":{"name":"Bell Nonlocality","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114429594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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