Summoning, No-Signaling and Relativistic Bit Commitments

TL;DR

This paper explores the summoning task in quantum and relativistic settings, showing how fundamental principles like no-cloning and no-signaling underpin the limits and security of quantum cryptographic protocols.

Contribution

It demonstrates that many summoning impossibility results and security proofs for cryptographic protocols follow from basic quantum and relativistic principles.

Findings

Summoning impossibility follows from no-cloning and no-signaling.

Bounds on approximate cloning fidelity are derived.

Cryptographic protocols can be secure against non-signaling adversaries.

Abstract

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.