Spatial quantum error correction threshold

Understand

We consider a spatial analogue of the quantum error correction threshold.

• Given individual time-independent subsystems in which quantum information is coherent over sufficiently long lengths, we show how the information can be kept coherent for arbitrarily long lengths by forming time-independent composite systems.
• The subsystem coherence length exhibits threshold behavior.
• When it exceeds a length ${\xi}_{th}$, meaningful information can be extracted from the ground state of the composite system.