Certification of genuinely entangled subspaces of the five qubit code via robust self-testing.

Abstract

Self-testing provides a device-independent framework for certifying quantum properties based solely on input-output statistics while treating quantum devices as black boxes. It has evolved significantly from its origins in bipartite systems to applications in multipartite entanglement and, more recently, genuinely entangled subspaces. Notably, It has been revealed that the logical subspaces of numerous stabilizer quantum error correction codes are exclusively composed of genuinely multipartite entangled states, opening new avenues for developing device-independent tools to characterize these subspaces. In this work, we leverage the self-testing technique to certify genuinely entangled logical subspaces within the five-qubit code using both photonic and superconducting platforms. This is achieved by preparing informationally complete logical states, simulating Pauli errors on a physical qubit, and testing several stabilizer-formalized Bell inequalities. Our certification is supported by an extractability measure of at least $0.828\pm0.006$ and $0.621\pm0.007$ for the photonic and superconducting systems, respectively. Our results demonstrate the feasibility of device-independent certification of general entangled quantum structures in experimental settings, extending beyond quantum states and quantum measurements.