Towards Asymptotically Tight Bounds Sample Clauses

Towards Asymptotically Tight Bounds. Recall that, by Definition 9, S(Q) denotes the secret-key rate in the setting where Alice’s and Bob’s channels are identical (i.e., sA = sB always), and Eve’s channel is exactly Q times better than both of Alice’s and Bob’s. Moreover, by Definition 10, R(Q) denotes the secret-key rate of the parity-check protocol in the same setting. In Sections 4.2 and 4.3, recalling also Definitions 7 and 8, we have overall proven the following bounds on S−(Q), S+(Q), S(Q), and R(Q): c Q2 ≤ R(Q) ≤ S(Q) ≤ S−(Q), ≤ ≤ Q2 Thus, in this setting we have determined the secret-key rate up to a multiplicative constant, proving the conjecture by Gander and Xxxxxx.
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