English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The robustness of quantum memory against physical noises is measured by twomethods: the exact and approximate quantum error correction (QEC) conditionsfor error recoverability, and the decoder-dependent error threshold whichassesses if the logical error rate diminishes with system size. Here we unraveltheir relations and propose a unified framework to extract an intrinsic errorthreshold from the approximate QEC condition, which could upper bound otherdecoder-dependent error thresholds. Our proof establishes that relativeentropy, effectively measuring deviations from exact QEC conditions, serves asthe order parameter delineating the transition from asymptotic recoverabilityto unrecoverability. Consequently, we establish a unified framework fordetermining the error threshold across both exact and approximate QEC codes,addressing errors originating from noise channels as well as those from codespace imperfections. This result sharpens our comprehension of error thresholdsacross diverse QEC codes and error models.

Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition