Encoding classical information into quantum resources

Understand

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.