  We construct a protocol for extracting distributed one-qubit quantum
information encoded in a stabilizer code of multiple qubits, only by
single-qubit local operations and classical communication (LOCC) without global
operations or entanglement resources. This protocol achieves efficient
extraction within a polynomial time in terms of the number of physical qubits.
We apply this protocol to a setting of quantum information splitting where a
subset of spatially separated parties cooperate by classical communication to
extract quantum information shared among all the parties. For this task, our
LOCC extraction protocol allows designing hierarchical information access
structures among the parties, where the minimum number of parties required to
cooperate depends on the location of extracting the shared quantum information.
These results provide a fundamental building block of distributed quantum
information processing that requires access to distributed quantum information
encoded in the stabilizer codes.
