A note on quantum error correction with continuous variables

Abstract

We demonstrate that continuous-variable quantum error correction based on Gaussian ancilla states and Gaussian operations (for encoding, syndrome extraction, and recovery) can be very useful to suppress the effect of non-Gaussian error channels. For a certain class of stochastic error models, reminiscent of those typically considered in the qubit case, quantum error correction codes designed for single-channel errors may enhance the transfer fidelities even when errors occur in every channel employed for transmitting the encoded state. In fact, in this case, the error-correcting capability of the continuous-variable scheme turns out to be higher than that of its discrete-variable analogues.

Keywords:

• quantum optics
• quantum information
• quantum communication
• continuous variables

Acknowledgements

The author acknowledges the Emmy Noether programme of the DFG in Germany. He also thanks Samuel Braunstein and Akira Furusawa for useful discussions.

Notes

Note

1. A non-Gaussian protocol is considered in Ref. 7, where a discrete-variable state can be encoded into a continuous-variable oscillator mode.