A correspondence between quantum error correcting codes and quantum reference frames

Understand

In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information.

• In a quantum error correcting code (QECC), a collection of computational degrees of freedom that make up a device's physical layer is used to redundantly encode a smaller amount of logical information.
• We elaborate this parallel in terms of quantum reference frames (QRFs), which are a universal toolkit for dealing with symmetries in quantum systems and which define the gauge theory analog of encodings.
• The result is a precise dictionary between QECCs and QRF setups within the perspective-neutral framework for gauge systems.