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Many papers on Quantum Key Distribution protocols discuss the protocols upper and lower bounds (on quantum bit error rate QBER).

For example, BB84 has a lower bound of 11% and an upper bound of ~14.6%.

What is the meaning of these bounds?

I believe that if the QBER is less than 11%, a secure key can be established, and if the QBER exceeds ~14.6% a secure key cannot be established, but what if the QBER is 12%? Does this mean that it is possible to create a secure key after error correction and privacy amplification, but prior to these being applied a secure key cannot be garuanteed?

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up vote 1 down vote accepted

Closing the gap between lower and upper bounds for the tolerated errors in quantum key distribution protocols is a long standing problem in the field.

In general, to give a lower bound on the key rate, one must provide a particular security proof of the protocol, but this proof may be suboptimal. For the BB84 protocol, the highest tolerable error rate I know of is 18.9%. On the other hand, from a simple intercept-resend attack, Eve can have full access to the key by introducing a 25% error rate, so this provides an upper bound.

Now, can the BB84 protocol tolerate 23% error rate? The simple answer is: We don't know! Clearly, for a given error rate, the key rate is either zero or non-zero, but there exist error rates for which we do not yet have security proofs that allow us to determine whether a secret key can be retrieved.

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