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Basically, the advantage is that you're creating the same one time pad in two faraway places at the same time, so there's no risk of it being intercepted. If Eve tries to mess with the stream of entangled photons all that will happen is that Alice and Bob will see garbage when they try to decrypt their message. If the one-time pad had been sent via traditional means, Eve would be able to read the message without Alice and Bob knowing.

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