We develop a theory of charge-parity-time (CPT) frameness resources to circumvent CPT-superselection. We construct and quantify such resources for spin~0, $frac{1}{2}$, 1, and Majorana particles and show that quantum information processing is possible even with CPT superselection. Our method employs a unitary representation of CPT inversion by considering the aggregate action of CPT rather than the composition of separate C, P and T operations, as some of these operations involve problematic anti-unitary representations.
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