TY - JOUR

T1 - Nonlinear quantum error correction

AU - Reichert, Maximilian

AU - Tessler, Louis W.

AU - Bergmann, Marcel

AU - van Loock, Peter

AU - Byrnes, Tim

PY - 2022/6

Y1 - 2022/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85133322856&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.105.062438

DO - 10.1103/PhysRevA.105.062438

M3 - Article

AN - SCOPUS:85133322856

SN - 2469-9926

VL - 105

SP - 062438-1-062438-11

JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information

JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information

IS - 6

M1 - 062438

ER -