Logical Bell-state protocols with d=3/5 surface and Bacon-Shor codes in ion traps need gate error rates around 10^-4 to 10^-5 to beat unencoded Bell states at 1 km, and the non-local protocol reaches about 33 Hz over 1 to 80 km.
Quantum repeaters and computation by a single module: Remote nondestructive parity measurement,
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Feasibility of Logical Bell State Generation in Memory Assisted Quantum Networks
Logical Bell-state protocols with d=3/5 surface and Bacon-Shor codes in ion traps need gate error rates around 10^-4 to 10^-5 to beat unencoded Bell states at 1 km, and the non-local protocol reaches about 33 Hz over 1 to 80 km.