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Threshold effect for probabilistic entanglement swapping
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DOI：10.1016/j.aop.2023.169257.png)
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The basic entanglement swapping protocol allows to project two qubits, which have never interacted, onto a maximally entan-gled state. For deterministic swapping, the key ingredient is the maximal entanglement that was initially contained in two pairs of qubits and the capacity of projecting onto a Bell basis. Thus the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we propose probabilistic entanglement swapping processes per-formed with different amounts of initial entanglement. Besides that we suggest a non Bell measuring-basis, to introduce a third entanglement level in the process. Additionally, we propose the unambiguous state extraction scheme as the local mechanism for probabilistically achieving the EPR projection. The combination of these three elements allows us to design four strategies for performing probabilistic entanglement swapping. Surprisingly, we find a twofold entanglement threshold effect related to the concurrence of the measuring-basis. Specifically, the maximal probability of accomplishing a EPR projection becomes a constant for concurrences higher than or equal to threshold entangle-ment value. Thus, we show that maximal entanglement in the measuring-basis is not required for attaining the EPR projection.(c) 2023 Published by Elsevier Inc.
Keyword:
Entanglement swapping
Entanglement swapping threshold
Probabilistic Entanglement swapping
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