Efficient decoding of stabilizer code by single-qubit local operations and classical communication

TL;DR

This paper presents a polynomial-time protocol for extracting quantum information encoded in stabilizer codes using only local operations and classical communication, enabling efficient distributed quantum information processing without global entanglement.

Contribution

The paper introduces a novel LOCC-based protocol for extracting stabilizer code-encoded quantum information efficiently, without global operations or entanglement resources.

Findings

Protocol achieves polynomial-time extraction of quantum information.

Enables hierarchical access structures among spatially separated parties.

Facilitates distributed quantum information processing without global entanglement.

Abstract

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.