基于优势互补的资源互换适度偏差分析
Moderate deviation analysis of majorisation-based resource interconversion
摘要：
我们考虑在所有理论中相互转换有限数量的资源的问题，这些理论的单发变换规则是基于一个优化关系的，例如，纠缠和相干的资源理论（对于纯态变换），以及热力学（对于能量不相干变换）。当只有有限的资源可用时，我们期望看到在资源状态$ρ$的$n$拷贝可以被转换成另一资源状态$σ$的$nr_n$拷贝的速率$r_n$与作为$n$的函数的相互转换过程的错误级别$\varepsilon_n$之间的非平凡的折衷。在这项工作中，我们得到了最佳的权衡，在所谓的适度偏差制度，其中的相互转换率$r_n$接近其最佳的无界资源（$n\to\infty$）的渐近极限，而错误$ε_n$消失在相同的限制。我们发现，中度偏差分析表现出共振行为，这意味着某些对资源状态可以相互转换的渐近最优速率与可忽略不计的误差，即使在有限的$n$制度。
英文摘要：
We consider the problem of interconverting a finite amount of resources within all theories whose single-shot transformation rules are based on a majorisation relation, e.g. the resource theories of entanglement and coherence (for pure state transformations), as well as thermodynamics (for energy-incoherent transformations). When only finite resources are available we expect to see a non-trivial trade-off between the rate $r_n$ at which $n$ copies of a resource state $ρ$ can be transformed into $nr_n$ copies of another resource state $σ$, and the error level $\varepsilon_n$ of the interconversion process, as a function of $n$. In this work we derive the optimal trade-off in the so-called moderate deviation regime, where the rate of interconversion $r_n$ approaches its optimum in the asymptotic limit of unbounded resources ($n\to\infty$), while the error $ε_n$ vanishes in the same limit. We find that the moderate deviation analysis exhibits a resonance behaviour which implies that certain pairs of resource states can be interconverted at the asymptotically optimal rate with negligible error, even in the finite $n$ regime.
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