Breaking the Storage-Bandwidth Tradeoff in Distributed Storage with Quantum Entanglement

TL;DR

This paper addresses the storage–bandwidth tradeoff in distributed storage by introducing an entanglement-assisted quantum repair model, where $d$ helper nodes share pre-established entanglement and send $eta_{ ext{q}}$ qudits to a newcomer that then measures to store $oldsymbol{ ext{alpha}}$ dits. It derives a quantum cut-set bound, $\sum_{i=0}^{k-1} \min\{2(d-i)\beta_{ ext{q}}, d\beta_{ ext{q}}, \alpha\} \ge B$, that characterizes the new tradeoff and exhibits quantum gains over the classical bound, especially at the MSR point for $d \le 2k-2$. A key finding is that when $d \ge 2k-2$, the quantum MSR and MB R points coincide, yielding a single optimal point that simultaneously minimizes storage and repair bandwidth, thereby breaking the classical tradeoff regime. For $d \le 2k-2$, entanglement-assisted repair reduces the required repair bandwidth at the MSR point (with explicit QMSR and QMBR expressions), illustrating substantial quantum advantages. The paper also provides concrete numerical examples demonstrating both regimes and discusses the practical impact of quantum communication in distributed storage systems.

Abstract

This work investigates the use of quantum resources in distributed storage systems. Consider an $(n,k,d)$ distributed storage system in which a file is stored across $n$ nodes such that any $k$ nodes suffice to reconstruct the file. When a node fails, any $d$ helper nodes transmit information to a newcomer to rebuild the system. In contrast to the classical repair, where helper nodes transmit classical bits, we allow them to send classical information over quantum channels to the newcomer. The newcomer then generates its storage by performing appropriate measurements on the received quantum states. In this setting, we fully characterize the fundamental tradeoff between storage and repair bandwidth (total communication cost). Compared to classical systems, the optimal storage--bandwidth tradeoff can be significantly improved with the enhancement of quantum entanglement shared only among the surviving nodes, particularly at the minimum-storage regenerating point. Remarkably, we show that when $d \geq 2k-2$, there exists an operating point at which \textit{both storage and repair bandwidth are simultaneously minimized}. This phenomenon breaks the tradeoff in the classical setting and reveals a fundamentally new regime enabled by quantum communication.

Figures (5)

• Figure 1: The classical and quantum cut for distributed storage system with $(n,k,d) = (4,2,3)$, $\alpha=3$, and $\beta_{\mathsf{c}} = \beta_{\mathsf{q}} = \beta = 1$.
• Figure 2: The per-node bandwidth ratio $\frac{\beta_{\mathsf{q}}^{\rm QMSR}}{\beta_{\mathsf{c}}^{\rm MSR}}$ versus the number of helper nodes $d$, when $n=50$, $k=10$.
• Figure 3: The per-node bandwidth ratio $\frac{\beta_{\mathsf{q}}^{\rm QMBR}}{\beta_{\mathsf{c}}^{\rm MBR}}$ versus the number of helper nodes $d$, when $n=50, k=10$.
• Figure 4: Comparison of the classical and quantum tradeoff for $n=8$, $k = 4$, $d = 7$, $B=1$. Since $d \geq 2k-2$, the QMSR point coincides with the QMBR point, yielding a single optimal regenerating point for the system.
• Figure 5: Comparison of the classical and quantum tradeoff curves for $n=15$, $k=10$, $d=14$, and $B=1$.

Theorems & Definitions (10)

• Remark 1
• Theorem 1
• Remark 2
• Corollary 1
• Remark 3
• Corollary 2
• Remark 4
• Remark 5: Optimal regenerating point
• Example 1
• Example 2