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Quantum bit error rate

Quantum Computing Asked by Rasha rashed on June 9, 2021

I am trying to understand the quantum key distribution and Quantum Bit Error Rate (QBER). I have question: Why is the QBER given by the average of the diagonals of the crosstalk matrix? Why the need to calculate the value using the diagonals?

One Answer

I do not know how the crosstalk matrix works. But the way I understand QBER is the following:

QBER is the mismatch probability of the signals sent and receieved between Alice and Bob. Let Alice send 100 signals to Bob. Bob makes his own measurement choices and at the end, they compare their results. Let's say, in 60 of these 100 signals, Bob measured in the 'right' basis, i.e., his result should match Alice's preparation. Meaning, in these 60 cases, if Alice intended to send classical bit 0 (or 1), Bob should receive classical bit 0 (or 1).

However, due to some unwanted noise (Eve!), among these 60 cases, some of their results differed. Let in 5 of these 60 cases, Alice wanted to send 0, Bob should have received 0 (because he made the right measurement choice), but got 1. The other case is also possible. I.e., let 7 of the 60 cases, Alice sent a 1, but Bob received 0. The QBER is then: $$ QBER = frac{5}{60} + frac{7}{60}. $$

Does it help a little? I welcome the community members to comment on this answer to confirm my understanding too!

Answered by Hasan Iqbal on June 9, 2021

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