Nonlinear quantum error correction

Maximilian Reichert, Louis W. Tessler, Marcel Bergmann, Peter van Loock, Tim Byrnes*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review


    We introduce a theory of quantum error correction (QEC) for a subclass of states. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords. However, this can be more general than required for a given quantum protocol which may only traverse a subclass of states within the Hilbert space. Here we propose the concept of nonlinear QEC (NLQEC), where the encoded states are not necessarily a linear combination of codewords. We introduce a sufficiency criterion for NLQEC with respect to the subclass of states. The new criterion gives a more relaxed condition for the formation of a QEC code, such that under the assumption that the states are within the subclass of states, the errors are correctable. This allows us, for instance, to effectively circumvent the no-go theorems regarding optical QEC for Gaussian states and channels, for which we present explicit examples.

    Original languageEnglish
    Article number062438
    Pages (from-to)062438-1-062438-11
    Number of pages11
    JournalPhysical Review A: covering atomic, molecular, and optical physics and quantum information
    Issue number6
    Publication statusPublished - Jun 2022


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