量子纠错阈值处临界指数的系综依赖性
Ensemble Dependence of the Critical Exponent at a Quantum Error Correction Threshold
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中文总结 AI 辅助
研究量子纠错阈值处临界指数对系综的依赖性，发现不同系综导致不同指数并饱和信息论界限，且转变存在性也依赖系综。
中文摘要 AI 辅助
在热力学中，通常假设在热力学极限下系综的选择（如微正则系综、正则系综或巨正则系综）不应影响底层物理。我们表明，这一假设对于临界指数未必成立。通过考察量子纠错的简化模型（由随机酉算子进行单步编码和解码）以及相应阈值处保真度和魔力的行为，我们发现使用通用信道或所谓等价的量子轨迹时会得到不同的指数。有趣的是，所获得的指数饱和了Feldman等人（2026）最近推导的信息论界限，我们将其从巨正则情形推广到正则情形，并包含了我们定义的中间系综。此外，我们进一步证明，转变的存在性本身也依赖于系综的选择。
英文摘要
In thermodynamics it is common to assume that the choice of ensemble (e.g., micro-canonical, canonical, or grand-canonical) should not affect the underlying physics in the thermodynamics limit. We show that this does not necessarily hold for critical exponents. Examining a simplified model of quantum error correction (single step encoding and decoding by a random unitary) and the behavior of both the fidelity and magic at the corresponding threshold, we find different exponents when using generic channels or supposedly equivalent quantum trajectories. Interestingly, the obtained exponents saturate a recently derived information theoretic bound by Feldman et al. (2026), which we extend from the grand-canonical to the canonical case, including intermediate ensembles which we define. Moreover, even the existence of the transition is shown to be ensemble-dependent.
发表机构
- School of Physics and Astronomy, Tel-Aviv University（特拉维夫大学物理与天文学院）
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