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In this paper, we investigate a terrestrial relay-assisted scheme for a free-space quantum key distribution (QKD) system based on BB84 protocol. We consider the deployment of passive relays which simply redirect the qubits to the next relay node or to the receiver without performing any measurement or detection process. Based on a near-field analysis, we derive an upper bound on quantum bit error rate (QBER) of the relay-assisted QKD system. Our results demonstrate that the relay-assisted scheme is able to outperform point-to-point direct transmission for long link ranges in which turbulence effects are particularly degrading.