We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore applications ranging from super-dense coding to thermodynamics. For any state, we find that the number of messages that can be encoded into it using such operations in a one-shot scenario is upper bounded in terms of the information spectrum relative entropy between the given state and its version with erased resources. Furthermore, if the resource destroying map is the twirling channel over some unitary group, we find matching one-shot lower bounds as well. In the asymptotic setting where we encode into many copies of the resource state, our bounds yield an operational interpretation of resource monotones such as the relative entropy of coherence and its corresponding relative entropy variance.

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 rnat which n copies of a resource state ρ can be transformed into nrncopies of another resource state σ, and the error level εnof 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 rnapproaches its optimum in the asymptotic limit of unbounded resources (n → ∞), while the error εnvanishes 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.