Quantum Entanglement Halves the Oblivious Update Bandwidth

We consider (n,k) MDS-coded distributed storage over mathbb{F}_q with per-node storage α 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 αk log₂ q bits. We prove that when the k contacted helpers share prior quantum entanglement, the update bandwidth is lceil α/2 rceil cdot k log₂ q bits-equivalent, a factor approaching 2 reduction. For α= 2, a [[k, k-2]]_q CSS code achieves bandwidth k log₂ q with one qudit per helper. For general α, a \[[lceil α/2 rceil k, lceil α/2 rceil k - α\]]_q CSS code achieves the bound with lceil α/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 D² distinguishable signals for dimension D. The result holds for all (n,k) pairs with sufficiently large prime q.