Simultaneously Minimizing Storage and Bandwidth Under Exact Repair With Quantum Entanglement

TL;DR

This paper demonstrates that the optimal trade-off point for minimizing storage and bandwidth in entanglement-assisted distributed storage systems under exact repair can be achieved using quantum and classical coding frameworks.

Contribution

It extends the optimal regenerating code results from functional to exact repair in quantum entanglement-assisted distributed storage systems.

Findings

Optimal point for storage and bandwidth is achievable under exact repair.

Construction uses classical product-matrix and CSS stabilizer formalism.

Results apply when the number of surviving nodes d is at least 2k-2.

Abstract

We study exact-regenerating codes for entanglement-assisted distributed storage systems. Consider an $(n,k,d,\alpha,\beta_{\mathsf{q}},B)$ distributed system that stores a file of $B$ classical symbols across $n$ nodes with each node storing $\alpha$ 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 $\beta_{\mathsf{q}}$ 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 $\alpha$ and repair bandwidth $d \beta_{\mathsf{q}}$} 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.