Robust bell inequalities from communication complexity
The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight low...
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2016
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_18688969_v61_n_p_Laplante http://hdl.handle.net/20.500.12110/paper_18688969_v61_n_p_Laplante |
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paper:paper_18688969_v61_n_p_Laplante2023-06-08T16:29:53Z Robust bell inequalities from communication complexity Bell inequalities Communication complexity Detector efficiency Nonlocality Bells Computational complexity Quantum computers Quantum cryptography Quantum theory Bell inequalities Bell-inequality violations Classical communication Communication complexity Detector efficiency Nonlocalities Quantum communication complexity Quantum distribution Quantum communication The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bounds. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities. © Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno; licensed under Creative Commons License CC-BY. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_18688969_v61_n_p_Laplante http://hdl.handle.net/20.500.12110/paper_18688969_v61_n_p_Laplante |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Bell inequalities Communication complexity Detector efficiency Nonlocality Bells Computational complexity Quantum computers Quantum cryptography Quantum theory Bell inequalities Bell-inequality violations Classical communication Communication complexity Detector efficiency Nonlocalities Quantum communication complexity Quantum distribution Quantum communication |
| spellingShingle |
Bell inequalities Communication complexity Detector efficiency Nonlocality Bells Computational complexity Quantum computers Quantum cryptography Quantum theory Bell inequalities Bell-inequality violations Classical communication Communication complexity Detector efficiency Nonlocalities Quantum communication complexity Quantum distribution Quantum communication Robust bell inequalities from communication complexity |
| topic_facet |
Bell inequalities Communication complexity Detector efficiency Nonlocality Bells Computational complexity Quantum computers Quantum cryptography Quantum theory Bell inequalities Bell-inequality violations Classical communication Communication complexity Detector efficiency Nonlocalities Quantum communication complexity Quantum distribution Quantum communication |
| description |
The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bounds. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities. © Sophie Laplante, Mathieu Laurière, Alexandre Nolin, Jérémie Roland, and Gabriel Senno; licensed under Creative Commons License CC-BY. |
| title |
Robust bell inequalities from communication complexity |
| title_short |
Robust bell inequalities from communication complexity |
| title_full |
Robust bell inequalities from communication complexity |
| title_fullStr |
Robust bell inequalities from communication complexity |
| title_full_unstemmed |
Robust bell inequalities from communication complexity |
| title_sort |
robust bell inequalities from communication complexity |
| publishDate |
2016 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_18688969_v61_n_p_Laplante http://hdl.handle.net/20.500.12110/paper_18688969_v61_n_p_Laplante |
| _version_ |
1768546042209370112 |