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Would Zero Knowledge Proof (ZKP) remove the need for Quantum Key Distribution? (QKD)

Since we no longer need keys to be passed around?

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    $\begingroup$ What is you own research? $\endgroup$ – Vadym Fedyukovych Nov 23 '18 at 8:50
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I do not immediately see how Zero Knowledge Proof could be used for secure transmission of information, and thus compete with Quantum Key Distribution (when trivially complemented with the One Time Pad for confidentiality and a Carter-Wegman hash for integrity).

Much less do I see how traditional ZKP could work absent some unproved mathematical assumption (like the difficulty of the Discrete Logarithm problem), when avoiding such assumption is the only advantage of QKD. In order to compete with QKD on these grounds, we would need a Quantum Zero Knowledge Proof; that has been studied.

Also, QKD is next to not used, with people far frow craving for it, thus removing the non-existent need for QKD is moot.

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