Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

TL;DR

This paper introduces covariant quantum error-correcting codes based on SU(2) representations that enable enhanced quantum sensing by surpassing the standard quantum limit through metrological entanglement.

Contribution

It generalizes thermodynamic codes to broader spin systems using angular momentum algebra, providing bounds on code inaccuracy under various noise models.

Findings

Codes protect probe states with quantum Fisher information exceeding the standard quantum limit.

The codes are covariant with transversal U(1) logical gates.

Bounds on code inaccuracy are established under generic noise and erasures.

Abstract

We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on ``thermodynamic codes" to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known $d$ sites, under independent and identically distributed noise, and under heralded $d$-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.