Entanglement-assisted concatenated quantum codes.

Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show significant advantages over standard concatenated quantum codes (CQCs). First, we prove that, unlike standard CQCs, EACQCs can beat the nondegenerate Hamming bound for entanglement-assisted quantum error-correction codes (EAQECCs). Second, we construct families of EACQCs with parameters better than the best-known standard quantum error-correction codes (QECCs) and EAQECCs. Moreover, these EACQCs require very few Einstein-Podolsky-Rosen (EPR) pairs to begin with. Finally, it is shown that EACQCs make entanglement-assisted quantum communication possible, even if the ebits are noisy. Furthermore, EACQCs can outperform CQCs in entanglement fidelity over depolarizing channels if the ebits are less noisy than the qubits. We show that the error-probability threshold of EACQCs is larger than that of CQCs when the error rate of ebits is sufficiently lower than that of qubits. Specifically, we derive a high threshold of 47% when the error probability of the preshared entanglement is 1% to that of qubits.

Land Use and Climate Change Altered the Ecological Quality in the Luanhe River Basin.

Monitoring and assessing ecological quality (EQ) can help to understand the status and dynamics of the local ecosystem. Moreover, land use and climate change increase uncertainty in the ecosystem. The Luanhe River Basin (LHRB) is critical to the ecological security of the Beijing-Tianjin-Hebei region. To support ecosystem protection in the LHRB, we evaluated the EQ from 2001 to 2020 based on the Remote Sensing Ecological Index (RSEI) with the Google Earth Engine (GEE). Then, we introduced the coefficient of variation, Theil-Sen analysis, and Mann-Kendall test to quantify the variation and trend of the EQ. The results showed that the EQ in LHRB was relatively good, with 61.08% of the basin rated as 'good' or 'excellent'. The spatial distribution of EQ was low in the north and high in the middle, with strong improvement in the north and serious degradation in the south. The average EQ ranged from 0.58 to 0.64, showing a significant increasing trend. Furthermore, we found that the expansion of construction land has caused degradation of the EQ, whereas climate change likely improved the EQ in the upper and middle reaches of the LHRB. The results could help in understanding the state and trend of the eco-environment in the LHRB and support decision-making in land-use management and climate change.