Optimal high-dimensional entanglement concentration in the bipartite scenario

• URL: http://arxiv.org/abs/2304.04890v1
• Date: Mon, 10 Apr 2023 22:36:49 GMT
• Title: Optimal high-dimensional entanglement concentration in the bipartite scenario
• Authors: L. Palma Torres, M. A. Sol\'is-Prosser, O. Jim\'enez, E. S. G\'omez, A. Delgado
• Abstract summary: entanglement concentration is the procedure where from $N$ copies of a partially entangled state, a single state with higher entanglement can be obtained. Getting a maximally entangled state is possible for $N=1$, but associated success probability can be extremely low. We study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for $N=1$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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. Getting a maximally entangled state is possible for $N=1$. However, the associated success probability can be extremely low while 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 $\mathcal{Q}$ 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 $\mathcal{Q}$. 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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