The resource theory of quantum reference frames: manipulations and monotones

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Every restriction on quantum operations defines a resource theory,
determining how quantum states that cannot be prepared under the restriction may be manipulated and used to circumvent the restriction. A superselection
rule is a restriction that arises through the lack of a classical reference frame. The states that circumvent it (the resource) are quantum reference
frames. We consider the resource theories that arise from three types of
superselection rule, associated respectively with lacking: (i) a phase
reference, (ii) a frame for chirality, and (iii) a frame for spatial
orientation. Focussing on pure unipartite quantum states, we identify the necessary and sufficient conditions for a deterministic transformation between two resource states to be possible and, when these conditions are not met, the maximum probability with which the transformation can be
achieved. We also determine when a particular transformation can be achieved reversibly in the limit of arbitrarily many copies and find the
maximum rate of conversion. (joint work with Gilad Gour)