Quantum Entanglement Halves the Oblivious Update Bandwidth

TL;DR

This paper demonstrates that quantum entanglement can significantly reduce the bandwidth needed for oblivious updates in distributed storage systems, approaching a factor of two improvement over classical bounds.

Contribution

It introduces quantum entanglement as a resource to halve the update bandwidth in distributed storage, providing explicit code constructions and a matching converse bound.

Findings

Quantum entanglement reduces update bandwidth by nearly half.

Explicit CSS code constructions achieve the theoretical bounds.

The superdense coding bound underpins the converse argument.

Abstract

We consider $(n,k)$ MDS-coded distributed storage over $\mathbb{F}_q$ with per-node storage $\alpha$ symbols. For the oblivious update problem, where a single message symbol changes and neither helpers nor the stale node know which, the classical lower bound is $\alpha k \log_2 q$ bits. We prove that when the $k$ contacted helpers share prior quantum entanglement, the update bandwidth is $\lceil \alpha/2 \rceil \cdot k \log_2 q$ bits-equivalent, a factor approaching 2 reduction. For $\alpha = 2$, a $[[k, k-2]]_q$ CSS code achieves bandwidth $k \log_2 q$ with one qudit per helper. For general $\alpha$, a $[[\lceil \alpha/2 \rceil k, \lceil \alpha/2 \rceil k - \alpha]]_q$ CSS code achieves the bound with $\lceil \alpha/2 \rceil$ qudits per helper. The matching converse uses the superdense coding bound: the stale node holds all transmitted qudits and hence the entangled partners, so each helper's channel supports at most $D^2$ distinguishable signals for dimension $D$. The result holds for all $(n,k)$ pairs with sufficiently large prime $q$.