Quantum error correction against photon loss using multi-component cat states

Abstract

We analyse a generalised quantum error correction code against photon loss where a logical qubit is encoded into a subspace of a single oscillator mode that is spanned by distinct multi-component cat states (coherent-state superpositions). We present a systematic code construction that includes the extension of an existing one-photon-loss code to higher numbers of losses. When subject to a photon loss (amplitude damping) channel, the encoded qubits are shown to exhibit a cyclic behaviour where the code and error spaces each correspond to certain multiples of losses, half of which can be corrected. As another generalisation we also discuss how to protect logical qudits against photon losses, and as an application we consider a one-way quantum communication scheme, in which the encoded qubits are periodically recovered while the coherent-state amplitudes are restored as well at regular intervals.

32 pages (15 pages Appendices) and 9 figures

References in corpus (7)

• New class of quantum error-correcting codes for a bosonic mode
• A No-Go Theorem for Gaussian Quantum Error Correction
• Fault-tolerant linear optical quantum computing with small-amplitude coherent states
• Quantum error correction against photon loss using NOON states
• Protecting an optical qubit against photon loss
• Could Gaussian regenerative stations act as quantum repeaters?
• Entanglement properties of optical coherent states under amplitude damping

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