On the probabilistic quantum error correction
Abstract
Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we deeply analyze probabilistic version of the error-correcting procedure for general noise. We generalized the Knill-Laflamme conditions for probabilistically correctable errors. We show that for some noise channels, we should encode the information into a mixed state to maximize the probability of successful error correction. Finally, we investigate an advantage of the probabilistic error-correcting procedure over the deterministic one. Reducing the probability of successful error correction allows for correcting errors generated by a broader class of noise channels. Significantly, if the errors are caused by a unitary interaction with an auxiliary qubit system, we can probabilistically restore a qubit state by using only one additional physical qubit.
Cite
@article{arxiv.2206.05232,
title = {On the probabilistic quantum error correction},
author = {Ryszard Kukulski and Łukasz Pawela and Zbigniew Puchała},
journal= {arXiv preprint arXiv:2206.05232},
year = {2023}
}
Comments
28 pages, 2 figures