Efficient Code for Relativistic Quantum Summoning

TL;DR

This paper develops a comprehensive mathematical framework and an efficient quantum summoning protocol for relativistic systems, optimizing encoding and decoding processes while respecting causality and no-cloning constraints.

Contribution

It introduces a new quantum summoning protocol based on Calderbank-Shor-Steane codes that improves space and gate complexity for relativistic quantum communication.

Findings

Reduces encoding space complexity by a factor of two.

Decreases gate complexity from cubic to quadratic in the number of causal diamonds.

Includes a decoding process with linear gate complexity.

Abstract

Summoning retrieves quantum information, prepared somewhere in spacetime, at another specified point in spacetime, but this task is limited by the quantum no-cloning principle and the speed-of-light bound. We develop a thorough mathematical framework for summoning quantum information in a relativistic system and formulate a quantum summoning protocol for any valid configuration of causal diamonds in spacetime. For single-qubit summoning, we present a protocol based on a Calderbank-Shor-Steane code that decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Our protocol includes decoding whose gate complexity scales linearly with the number of causal diamonds. Our thorough framework for quantum summoning enables full specification of the protocol, including spatial and temporal implementation and costs, which enables quantum summoning to be a well posed protocol for relativistic quantum communication purposes.