Self-catalytic conversion of pure quantum states

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Conversion of entangled states under (stochastic) local operations and classical communication ((S)LOCC) admits the phenomenon of catalysis. Here we explore the possibility of a copy of the initial state itself performing as a catalyst, which we call a self-catalytic process. We show explicit examples of self-catalysis. Necessary and sufficient conditions for the phenomenon to take place are discussed. We numerically estimate how frequent it is and we show that increasing the number of copies used as catalyst can increase the probability of conversion, but does not make the process deterministic. By the end we conjecture that under LOCC the probability of finding a self-catalytic reaction does not increase monotonically with the dimensions whereas under SLOCC, it does increase.