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. 2018 Oct 4;8:14793. doi: 10.1038/s41598-018-33125-3

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Quantum circuit diagram for the protocol of two interacting individuals. Squares with a continuous line denote the phase values of u₃ gate, while squares with a dashed line denote the phase values of u₂ gate, both in units of π. When possible we reduce the expression to the value of θ and avoid writing the additional phases.