Jonathan Matthew Chadbourne · JCEE Labs
How much communication makes perfect recovery possible?
Two separated holders of quantum side information are asked to recover the same complete BB84 measurement outcome after the basis string is publicly revealed. The paper studies how much classical communication they need, and what a limited one-message budget permits.
An external reviewer has recommended major revision and offered to reassess the manuscript. The public PDF remains a preprint; the review is not publication acceptance or peer-reviewed validation. No claim of novelty or priority is established by this release.
Results, with their assumptions attached
The paper establishes the exact perfect-recovery cost c_min(n) = n for finite-round classical interaction, together with a bounded-error converse. For one-message protocols, its lower and upper bounds meet at c = n − 1: the optimal success probability is Q = cos²(π/8) for every n ≥ 1. This includes the one-message (2,1) case; the interactive (2,1) case has the same value under the stated cost convention.
The model permits arbitrary finite-dimensional prior entanglement prepared independently of the later basis choice. The basis is uniform and publicly revealed. Success means that both receivers recover the entire outcome string. Post-split quantum communication is excluded. Classical communication uses the manuscript’s worst-case cost convention, including informative timing, speaker choice, and stopping.
The PDF gives the precise statements, proofs, bounded-error formula, one-message inequalities, and message-block projector argument. This overview does not replace those definitions.
What remains open
The general one-message interior frontier, interactive near-full recovery for n ≥ 3, and the exact physical one-message (3,1) case remain open. P0.45 R1 remains on hold.
The perfect-recovery theorem does not settle the general guessing frontier. The external review does not establish publication acceptance, practical cryptographic security, or a production implementation.
Read the released paper
A stable, identifiable release
This page presents the authorized October 1, 2026 v0.4-P2 release unchanged. Its accepted mathematical claims are frozen; this website publication is not a manuscript revision or a new research result.
Original manuscript: September 21, 2026. Public release: October 1, 2026. Version: v0.4-P2.
PDF SHA-256: 63e3a02f11cce223d4ff803f136baace51ee5839b04d0b04abec737910b4da20
Original public release mirror ↗
Cite as: Chadbourne, Jonathan Matthew. “Classical Communication in BB84 Monogamy Games: Perfect Recovery and One-Message Bounds.” JCEE Labs, public preprint v0.4-P2, October 1, 2026.