Higher transmission loss diminishes the performance of opticalcommunication|be it the rate at which classical or quantum data can be sentreliably, or the secure key generation rate of quantum key distribution (QKD).Loss compounds with distance|exponentially in an optical fiber, andinverse-square with distance for a free-space channel. In order to boostclassical communication rates over long distances, it is customary to introduceregenerative relays at intermediate points along the channel. It is thereforenatural to speculate whether untended regenerative stations, such asphase-insensitive or phase-sensitive optical amplifiers, could serve asrepeaters for long-distance QKD. The primary result of this paper rules out allbosonic Gaussian channels to be useful as QKD repeaters, which includephase-insensitive and phase-sensitive amplifiers as special cases, for any QKDprotocol. We also delineate the conditions under which a Gaussian relay rendersa lossy channel entanglement breaking, which in turn makes the channel uselessfor QKD.
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