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In a study published in , researchers have achieved device-independent characterization of genuinely entangled subspaces (GESs) in both optical and superconducting quantum systems, completing the self-checking of the five-qubit error correction code space.

In quantum information, genuinely multipartite entangled states require the existence of entanglement correlations between any two subsystems within the system. The GES constituted by the states has application value especially in designing quantum error-correcting codes. By encoding quantum information in the subspace, it can prevent error propagation caused by local decoherence.

Scientists have constructed a new Bell inequality based on the stabilizer code framework constructed, and the entangled subspace can be universally characterized by using it. Any quantum state (including mixed states) within this subspace could maximally violate this inequality, providing a theoretical basis for the self-testing of genuine entangled subspaces.

In this study, to verify the inequality, the researchers conducted two proof-of-principle experiments implementing the five-qubit code using both photonic and superconducting platforms. They achieved the device-independent certification of the five-qubit quantum error correction code space.

During the verifying process, researchers prepared a series of logical quantum states and conducted Bell tests. They found that the logical subspace fidelity of the two systems reached over 82% and 62%, respectively. This process relied solely on the data observed in the experiment without requiring trustworthy assumptions about the experimental equipment.

For the experiments on photonic and superconducting platforms, the researchers simulated a single physical bit error scenario and found that the logical state completely lost its ability to violate the Bell's inequality, demonstrating that it had deviated from the target logical subspace.

By further verifying the Bell inequality corresponding to the error subspaces, researchers successfully monitored the evolution of logical quantum state space.

The study demonstrates the feasibility of device-independent certification of general entangled quantum structures in experimental settings, extending beyond quantum states and quantum measurements. The research teams were led by Guo Guangcan and Prof. Liu Biheng from the University of Science and Technology of China (USTC) of the Chinese Academy of Sciences, collaborating with Origin Quantum Computing Company Limited.