Safeguarding Oscillators and Qudits with Distributed Two-Mode Squeezing

Recent advancements in multi-mode Gottesman-Kitaev-Preskill (GKP) codes have shown great promise in enhancing the protection of both discrete and analog quantum information. This broadened range of protection brings opportunities beyond quantum computing to benefit quantum sensing by safeguarding squeezing — the essential resource in many quantum metrology protocols. However, the potential for quantum sensing to benefit quantum error correction has been less explored. In this work, we provide a unique example where techniques from quantum sensing can be applied to improve multi-mode GKP codes. Inspired by distributed quantum sensing, we propose the distributed two-mode squeezing (dtms) GKP codes that offer benefits in error correction with minimal active encoding operations. Indeed, the proposed codes rely on a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi>g</mml:mi><mml:mi>l</mml:mi><mml:mi>e</mml:mi></mml:math> (active) two-mode squeezing element and an array of beamsplitters that effectively distributes continuous-variable correlations to many GKP ancillae, similar to continuous-variable distributed quantum sensing. Despite this simple construction, the code distance achievable with dtms-GKP qubit codes is comparable to previous results obtained through brute-force numerical search \cite{lin2023closest}. Moreover, these codes enable analog noise suppression beyond that of the best-known two-mode codes \cite{noh2020o2o} without requiring an additional squeezer. We also provide a simple two-stage decoder for the proposed codes, which appears near-optimal for the case of two modes and permits analytical evaluation.