High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell's Theorem

Author(s)

Martinez, Daniel ^{[1, 2]} ; Tavakoli, Armin ^[3] ; Casanova, Mauricio ^{[1, 2]} ; Canas, Gustavo ^[4] ; Marques, Breno ^{[5, 6]} ; Lima, Gustavo ^{[1, 2]}

Affiliation

^[1] Univ Concepcion, Dept Fis, 160-C, Concepcion - Chile

^[2] Univ Concepcion, Millennium Inst Res Opt, 160-C, Concepcion - Chile

^[3] Univ Geneva, Grp Phys Appl, CH-1211 Geneva - Switzerland

^[4] Univ Bio Bio, Dept Fis, Ave Collao 1202, Concepcion - Chile

^[5] Univ Sao Paulo, Inst Fis, BR-05315970 Sao Paulo - Brazil

^[6] Univ Fed ABC, Ctr Ciencias Nat & Humanas, Ave Estados 5001, BR-09210580 Sao Paulo - Brazil

• Document type: Journal article
• Source: Physical Review Letters; v. 121, n. 15 OCT 12 2018.
• Web of Science Citations: 5

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. (AU)

• FAPESP's process: 14/27223-2 - Control of quantum information with continuous variables of light beams
• Grantee: Breno Marques Goncalves Teixeira
• Support Opportunities: Scholarships in Brazil - Post-Doctoral