Moderate deviation analysis of majorisation-based resource interconversion

Abstract

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 $\rho$ can be transformed into $n{r}_n$ copies of another resource state $\sigma$, and the error level ${\epsilon }_n$ 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 ${\epsilon }_n$ 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.

arXiv comment16 pages, 1 figure. Comments welcome

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Cited by in corpus (11)

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• Avoiding irreversibility: engineering resonant conversions of quantum resources
• Coherence manipulation with dephasing-covariant operations
• The variance of relative surprisal as single-shot quantifier
• Fluctuation-dissipation relations for thermodynamic distillation processes
• Moderate deviation expansion for fully quantum tasks
• A hierarchy of thermal processes collapses under catalysis
• Quantum dichotomies and coherent thermodynamics beyond first-order asymptotics