  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.

Quantum Physics