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Martínez D, Tavakoli A, Casanova M, Cañas G, Marques B, Lima G. High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell's Theorem. PHYSICAL REVIEW LETTERS 2018; 121:150504. [PMID: 30362799 DOI: 10.1103/physrevlett.121.150504] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Indexed: 06/08/2023]
Abstract
Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission, and measurement of a single quantum system, in other words, quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realize such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the postquantum Bell correlations obeying only locality in the macroscopic limit. We find that the advantages are tied to the use of measurements that are not rank-one projective, and provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.
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Affiliation(s)
- Daniel Martínez
- Departamento de Física, Universidad de Concepción, 160-C Concepción, Chile
- Millennium Institute for Research in Optics, Universidad de Concepción, 160-C Concepción, Chile
| | - Armin Tavakoli
- Groupe de Physique Appliquée, Université de Genève, CH-1211 Genève, Switzerland
| | - Mauricio Casanova
- Departamento de Física, Universidad de Concepción, 160-C Concepción, Chile
- Millennium Institute for Research in Optics, Universidad de Concepción, 160-C Concepción, Chile
| | - Gustavo Cañas
- Departamento de Física, Universidad del Bio-Bio, Avenida Collao 1202, Concepción, Chile
| | - Breno Marques
- Instituto de Física, Universidade de São Paulo, 05315-970 São Paulo, Brazil
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
| | - Gustavo Lima
- Departamento de Física, Universidad de Concepción, 160-C Concepción, Chile
- Millennium Institute for Research in Optics, Universidad de Concepción, 160-C Concepción, Chile
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Li W, Zhao S. Bell's inequality tests via correlated diffraction of high-dimensional position-entangled two-photon states. Sci Rep 2018; 8:4812. [PMID: 29556069 PMCID: PMC5859148 DOI: 10.1038/s41598-018-23310-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Accepted: 03/08/2018] [Indexed: 11/12/2022] Open
Abstract
Bell inequality testing, a well-established method to demonstrate quantum non-locality between remote two-partite entangled systems, is playing an important role in the field of quantum information. The extension to high-dimensional entangled systems, using the so-called Bell-CGLMP inequality, points the way in measuring joint probabilities, the kernel block to construct high dimensional Bell inequalities. Here we show that in theory the joint probability of a two-partite system entangled in a Hilbert space can be measured by choosing a set of basis vectors in its dual space that are related by a Fourier transformation. We next propose an experimental scheme to generate a high-dimensional position-entangled two-photon state aided by a combination of a multiple-slit and a 4 f system, and describe a method to test Bell’s inequality using correlated diffraction. Finally, we discuss in detail consequences of such Bell-test violations and experimental requirements.
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Affiliation(s)
- Wei Li
- Nanjing University of Posts and Telecommunications, Institute of Signal Processing and Transmission, Nanjing, 210003, China. .,Sunwave Communications CO, Hangzhou, 310053, China.
| | - Shengmei Zhao
- Nanjing University of Posts and Telecommunications, Institute of Signal Processing and Transmission, Nanjing, 210003, China.,Nanjing University of Posts and Telecommunications, Key Lab Broadband Wireless Communication and Sensor, Network, Ministy of Education, Nanjing, 210003, China
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Cong W, Cai Y, Bancal JD, Scarani V. Witnessing Irreducible Dimension. PHYSICAL REVIEW LETTERS 2017; 119:080401. [PMID: 28952755 DOI: 10.1103/physrevlett.119.080401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2016] [Indexed: 06/07/2023]
Abstract
The Hilbert space dimension of a quantum system is the most basic quantifier of its information content. Lower bounds on the dimension can be certified in a device-independent way, based only on observed statistics. We highlight that some such "dimension witnesses" capture only the presence of systems of some dimension, which in a sense is trivial, not the capacity of performing information processing on them, which is the point of experimental efforts to control high-dimensional systems. In order to capture this aspect, we introduce the notion of irreducible dimension of a quantum behavior. This dimension can be certified, and we provide a witness for irreducible dimension four.
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Affiliation(s)
- Wan Cong
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Yu Cai
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Jean-Daniel Bancal
- Quantum Optics Theory Group, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Valerio Scarani
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117551, Singapore
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