Catalytic quantum randomness as a correlational resource

Catalysts are substances that assist transformation of other resourceful objects without being consumed in the process. However, fact their ``catalytic power'' is limited and can be depleted often overlooked, especially recently developing theories on catalysis quantum randomness utilizing building correlation with catalyst. In this work, we establish a resource theory one-shot catalytic which uncorrelatedness randomness. We do so by completely characterizing bipartite unitary operators used to implement using partial transpose. By doing so, find every channel factorizable, therefore there exists unital not catalytic. define family entropies quantifies catalytically extractable R\'enyi from state show how much degeneracy boost entropy beyond its ordinary entropy. Based this, demonstrate source actually exhausted after certain amount extracted. apply systems under superselection rules forbids superposition states nonmaximally mixed yield maximal discuss implications various topics, including absorption, no-secret theorem, possibility multiparty infinite catalysis.