Hi all,
Tomorrow we have a guest speaker, Marco Tomamichel from UTS in Sydney.
He’ll tell us about “Encoding classical information into quantum
resources”. See the abstract below.
Best,
-joe
Abstract: 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 a 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.