Quantum Error Correction in Pauli Channels Based on Redundancy, Weak Measurements and Entangled Rotations

Noisy channels alter the information on qubits transmitted through them, thereby significantly reducing communication fidelity. While most quantum error correction protocols employ a high number of redundant systems, we present a redundancy-based routine utilising weak measurements and entangled rotations that improves transmission fidelity in Pauli channels with only one redundant qubit. Each correction step enhances the outcome. In this research, output fidelity, together with the success probability of the weak measurement, is used to assess our performance analysis. Furthermore, the process of determining the optimal rotation angles for the final part of the procedure is also central to the analysis. A fidelity of 60% is achieved for most Pauli channels and Bloch sphere pure states. For certain emblematic channels, such as those present in current technologies, this fidelity increases to nearly 100%. Additionally, for these latter channels, our analysis reveals that the optimal angles belong to a reduced set, thereby offering a passive strategy based on channel characterisation. Furthermore, a study using the states in traditional QKD demonstrates that the aforementioned optimal angles can also be passively employed for correction. Finally, we propose a photonic experimental setup based on SPDC-generated entangled photons and Mach–Zehnder interferometry to implement a proof-of-principle.