Self-catalytic conversion of pure quantum states

TL;DR

This paper investigates self-catalytic processes in quantum state conversion, where copies of the initial state facilitate entanglement transformation, revealing conditions, frequency, and dimensional effects of such phenomena.

Contribution

It introduces the concept of self-catalysis in quantum state conversion, providing explicit examples, conditions, and numerical estimates of its frequency and dimensional behavior.

Findings

Self-catalysis can occur in quantum state conversion.

Increasing catalyst copies raises conversion probability but not deterministically.

Probability of self-catalysis varies with system dimensions under LOCC and SLOCC.

Abstract

Conversion of entangled states under (Stochastic) Local Operations and Classical Communication admits the phenomenon of catalysis. Here we explore the possibility of a copy of the initial state itself to perform 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 increases the probability of conversion, but do 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 SLOCC does increase.