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No-go theorem for device-independent security in relativistic causal theories

R. Salazar, M. Kamoń, K. Horodecki, D. Goyeneche, D. Saha, R. Ramanathan, and P. Horodecki
Phys. Rev. Research 3, 033146 – Published 13 August 2021
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Abstract

A fundamental question in device-independent quantum cryptography is to determine the minimal physical principle upon which the security of such a cryptographic protocol (such as for key distribution or for randomness generation) may be based. Since the seminal work on device-independent quantum key distribution by J. Barrett, L. Hardy, and A. Kent [Phys. Rev. Lett. 95, 010503 (2005)], a conjectured candidate for certification of device-independent security has been the principle of relativistic causality, namely the disallowance of causal loops. While this principle has thus far been equated with the no-signaling constraints, it has been shown recently that in multiparty Bell scenarios, the no-signaling constraints are sufficient but not necessary for relativistic causality, and a refined set of constraints has been proposed that more precisely capture the notion of relativistic causality. In this paper, we build upon this finding to show that, in contrast to the no-signaling constraints, the constraints of relativistic causality are not sufficient for certification of device-independent security. More specifically, we show that there exist correlations allowed by the causality principle that allow an adversary to gain complete information about the measurement outcomes of honest parties in any device-independent cryptographic protocol, thereby rendering the protocol completely insecure. As a tool to develop this adversarial attack strategy, we fully characterize the set of correlations allowed by relativistic causality in the tripartite Bell scenario of three parties, each performing two binary measurements, that may be of independent interest. We also demonstrate the difference between the relativistic causal correlations and those allowed by the usual no-signaling constraints by presenting explicit communication tasks wherein the two sets exhibit striking difference in their respective winning probabilities.

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  • Received 25 May 2021
  • Accepted 28 June 2021

DOI:https://doi.org/10.1103/PhysRevResearch.3.033146

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

R. Salazar1,2,3,4,*, M. Kamoń2, K. Horodecki3,5, D. Goyeneche6, D. Saha1,7, R. Ramanathan8, and P. Horodecki2,5

  • 1Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, University of Gdansk, 80-308 Gdansk, Poland
  • 2Faculty of Applied Physics and Mathematics, National Quantum Information Centre, Gdansk University of Technology, 80-233 Gdansk, Poland
  • 3Institute of Informatics Faculty of Mathematics, Physics, and Informatics, University of Gdansk, 80-308 Gdansk, Poland
  • 4Institute of Physics, Jagiellonian University, 30-059 Krakow, Poland
  • 5International Centre for Theory of Quantum Technologies, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland
  • 6Departamento de Física, Facultad de Ciencias Básicas, Universidad de Antofagasta, Casilla 170, Antofagasta, Chile
  • 7Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
  • 8Department of Computer Science, University of Hong Kong, Pokfulam Road, Hong Kong

  • *rb.salazar.vargas@gmail.com

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Issue

Vol. 3, Iss. 3 — August - October 2021

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