Effect on a QKD Chain Going Through a Generic Pauli Channel Together with a Correction Based on the 3-qubit Code

Abstract

Quantum cryptography is an emergent area in quantum technologies to set secure communication. BB84 protocol is a procedure to exchange a secure key to encode communication in the form of a chain of quantum bits. In this work, we model the non-ideal transmission of such a key through a parametric family of noisy channels: Pauli channels (including Bit-flipping and Dephasing noises). Assuming that Quantum Key Distribution is performed under such protocol, we analyse the fidelity of the transmission and the probability distribution for the imperfect outcomes. The analysis also includes the application of the quantum error correction algorithm: the 3-qubit code. Finally, we add the presence of an eavesdropper getting his conditional success rate to become unnoticed. The agreement in the basis selection between the transmitter and receiver is assumed as under a tentative reconciliation procedure. Outcomes show just positive effects on the transmission between sender and receiver, but a mild improvement for the success probability for the eavesdropper.