Simultaneously Minimizing Storage and Bandwidth Under Exact Repair With Quantum Entanglement

2026-05-12

AI Summary

This work addresses the problem of simultaneously minimizing per-node storage overhead α and repair bandwidth dβ_q in quantum entanglement-assisted distributed storage systems under exact repair conditions. By integrating the classical product-matrix framework with CSS-type stabilizer codes, the authors construct a novel class of quantum exact regenerating codes. In this scheme, d surviving nodes share entangled states and transmit quantum systems to a newcomer, which then performs measurements to exactly reconstruct the data stored on the failed node. The study establishes, for the first time, that when d ≥ 2k−2, this construction achieves the theoretical lower bounds on both storage and repair bandwidth simultaneously, thereby surpassing prior limitations restricted to functional repair and demonstrating the attainability of this optimal regeneration point under exact repair.

Abstract

We study exact-regenerating codes for entanglement-assisted distributed storage systems. Consider an $(n,k,d,α,β_{\mathsf{q}},B)$ distributed system that stores a file of $B$ classical symbols across $n$ nodes with each node storing $α$ symbols. A data collector can recover the file by accessing any $k$ nodes. When a node fails, any $d$ surviving nodes share an entangled state, and each of them transmits a quantum system of $β_{\mathsf{q}}$ qudits to a newcomer. The newcomer then performs a measurement on the received quantum systems to generate its storage. Recent work [1] showed that, under functional repair where the regenerated content may differ from that of the failed node, there exists a unique optimal regenerating point that \emph{simultaneously minimizes both storage $α$ and repair bandwidth $d β_{\mathsf{q}}$} when $d \geq 2k-2$. In this paper, we show that, under \emph{exact repair}, where the newcomer reproduces exactly the same content as the failed node, this optimal point remains achievable. Our construction builds on the classical product-matrix framework and the Calderbank-Shor-Steane (CSS)-based stabilizer formalism.

Problem

• exact repair
• distributed storage
• quantum entanglement
• regenerating codes
• repair bandwidth

Innovation

• exact repair
• quantum entanglement
• regenerating codes
• CSS stabilizer formalism
• product-matrix construction