Simultaneously Minimizing Storage and Bandwidth Under Exact Repair With Quantum Entanglement
It extends the optimal trade-off between storage and repair bandwidth from functional to exact repair in quantum-assisted distributed storage, a non-trivial but incremental step for the distributed storage community.
This paper shows that for entanglement-assisted distributed storage systems under exact repair, the optimal regenerating point that simultaneously minimizes storage and repair bandwidth (achieved previously only under functional repair) remains achievable. The construction uses the product-matrix framework and CSS-based stabilizer formalism.
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.