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Open AccessArticle

Summoning, No-Signalling and Relativistic Bit Commitments

by Adrian Kent 1,2
1
Centre for Quantum Information and Foundations, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
2
Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada
Entropy 2019, 21(5), 534; https://doi.org/10.3390/e21050534
Received: 22 March 2019 / Revised: 13 May 2019 / Accepted: 18 May 2019 / Published: 25 May 2019
(This article belongs to the Special Issue Relativistic Quantum Information)
Summoning is a task between two parties, Alice and Bob, with distributed networks of agents in space-time. Bob gives Alice a random quantum state, known to him but not her, at some point. She is required to return the state at some later point, belonging to a subset defined by communications received from Bob at other points. Many results about summoning, including the impossibility of unrestricted summoning tasks and the necessary conditions for specific types of summoning tasks to be possible, follow directly from the quantum no-cloning theorem and the relativistic no-superluminal-signalling principle. The impossibility of cloning devices can be derived from the impossibility of superluminal signalling and the projection postulate, together with assumptions about the devices’ location-independent functioning. In this qualified sense, known summoning results follow from the causal structure of space-time and the properties of quantum measurements. Bounds on the fidelity of approximate cloning can be similarly derived. Bit commitment protocols and other cryptographic protocols based on the no-summoning theorem can thus be proven secure against some classes of post-quantum but non-signalling adversaries. View Full-Text
Keywords: relativistic quantum information; quantum cryptography; summoning; no-cloning; no-signalling; bit commitment relativistic quantum information; quantum cryptography; summoning; no-cloning; no-signalling; bit commitment
MDPI and ACS Style

Kent, A. Summoning, No-Signalling and Relativistic Bit Commitments. Entropy 2019, 21, 534.

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