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Journal Article

Quantum Error-Correcting Codes for Qudit Amplitude Damping


Grassl,  Markus
Quantumness, Tomography, Entanglement, and Codes, Emeritus Group Leuchs, Emeritus Groups, Max Planck Institute for the Science of Light, Max Planck Society;

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Grassl, M., Kong, L., Wei, Z., Yin, Z.-Q., & Zeng, B. (2018). Quantum Error-Correcting Codes for Qudit Amplitude Damping. IEEE Transactions on Information Theory, 64(6), 4674-4685. doi:10.1109/TIT.2018.2790423.

Cite as: http://hdl.handle.net/21.11116/0000-0006-DF5B-A
Traditional quantum error-correcting codes are designed for the depolarizing channel modeled by generalized Pauli errors occurring with equal probability. Amplitude damping channels model, in general, the decay process of a multilevel atom or energy dissipation of a bosonic system at zero temperature. We discuss quantum error-correcting codes adapted to amplitude damping channels for higher dimensional systems (qudits). For multi-level atoms, we consider a natural kind of decay process, and for bosonic systems,we consider the qudit amplitude damping channel obtained by truncating the Fock basis of the bosonic modes to a certain maximum occupation number. We construct families of single-error-correcting quantum codes that can be used for both cases. Our codes have larger code dimensions than the previously known single-error-correcting codes of the same lengths. Additionally, we present families of multi-error correcting codes for these two channels, as well as generalizations of our construction technique to error-correcting codes for the qutrit V and Lambda channels.