Approximate recovery with locality and symmetry constraints

Understand

Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable operations.

• Moreover, these constraints combine non-trivially with the potential requirement that operations be performed locally.
• The combination of symmetry and locality constraints influence our ability to perform quantum error correction in two counterposing ways.
• On the one hand, they constrain the effect of noise, limiting its possible action over the quantum system.