# Protecting quantum entanglement between error-corrected logical qubits

## TL;DR

This paper demonstrates the experimental creation and protection of entangled logical qubits using quantum error correction, significantly enhancing coherence time and violating Bell inequality, advancing quantum information processing.

## Contribution

It introduces the first experimental realization of entangled logical qubits protected by quantum error correction, improving coherence and demonstrating Bell inequality violation.

## Key findings

- Coherence time of entangled logical qubits increased by 45%
- Bell inequality violation achieved with logical qubits, B=2.250
- Error correction extends entanglement robustness in quantum systems

## Abstract

Entanglement represents one of the most important conceptual advances in physics during the last century and is also one of the most essential resources in quantum information science. However, entanglement is fragile and its potential advantages in applications are hindered by decoherence in practice. Here, we experimentally realize entangled logical qubits (ELQ) with a bosonic quantum module by encoding quantum information into spatially separated microwave modes. The entanglement is protected by repetitive quantum error correction, and the coherence time of the purified ELQ via error detection is improved by 45$\%$ compared with the unprotected ELQ and exceeds that of the entangled physical qubits. In addition, violation of the Bell inequality by logical qubits is demonstrated for the first time with the measured Bell signal B=2.250$\pm$0.019 after purification, surpassing the classical bound by 13 standard deviations. The protected ELQ could be applied in future explorations of quantum foundations and applications of quantum networks.