Encoding Classical Information Into Quantum Resources

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