We extend the asymptotic security of continuous variable quantum key distribution using one-way and two-way quantum communication to a multi-way setting: Quantum signals travel many times between the parties before the final detection. We assume that the encoded signals are Gaussian-modulated coherent states that travel each time through the same Gaussian channel characterized by loss and thermal noise. We then quantify the reverse-reconciliation performance of the protocol presenting results for even or odd numbers of signal exchange.
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