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Considering pure quantum states, entanglement concentration is the procedurewhere from $N$ copies of a partially entangled state, a single state withhigher entanglement can be obtained. Getting a maximally entangled state ispossible for $N=1$. However, the associated success probability can beextremely low while increasing the system's dimensionality. In this work, westudy two methods to achieve a probabilistic entanglement concentration forbipartite quantum systems with a large dimensionality for $N=1$, regarding areasonably good probability of success at the expense of having a non-maximalentanglement. Firstly, we define an efficiency function $\mathcal{Q}$considering a tradeoff between the amount of entanglement (quantified by theI-Concurrence) of the final state after the concentration procedure and itssuccess probability, which leads to solving a quadratic optimization problem.We found an analytical solution, ensuring that an optimal scheme forentanglement concentration can always be found in terms of $\mathcal{Q}$.Finally, a second method was explored, which is based on fixing the successprobability and searching for the maximum amount of entanglement attainable.Both ways resemble the Procrustean method applied to a subset of the mostsignificant Schmidt coefficients but obtaining non-maximally entangled states.

Optimal high-dimensional entanglement concentration in the bipartite scenario