Quantum Stabilizer Codes Embedding Qubits Into Qudits

Abstract

We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to protect the qubit against both amplitude and phase errors. The performance of such code is evaluated on Weyl channels by means of the entanglement fidelity as function of the error probability. A comparison with standard block codes, like five and seven qubit stabilizer codes, shows its superiority.

15 pages, 2 figures (improved version); accepted for publication in Phys. Rev. A