Optimal High-Dimensional Entanglement Concentration for Pure Bipartite Systems.

Micromachines (Basel)

Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción 4070043, Chile.

Published: June 2023

Considering pure quantum states, entanglement concentration is the procedure where, from copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N=1. 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 N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q 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 Q. 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.

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Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10303354PMC
http://dx.doi.org/10.3390/mi14061207DOI Listing

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