Abstract

Considering pure quantum states, entanglement concentration is the procedure where, from N copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for (Formula presented.). However, the associated success probability can be extremely low when increasing the system’s dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for (Formula presented.), regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function (Formula presented.) considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of (Formula presented.). Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states. © 2023 by the authors.