2026/06/30 by Kenny Chen · 1 voice
Computer Science · #quant-ph #cs.DS
Recently, Doosti et al. introduced the problem of distributed quantum state verification, where m distributed nodes are given a copy of an unknown state ρ, and can send limited one way communication to a central node, who has a complete description of a known state σ. They ask how many distributed nodes m are required, before the central node can succeed at distinguishing whether ρ=σ or ‖ρ-σ‖1≥ε with high probability. In the setting where only quantum communication is allowed, Doosti et al. exhibit conditional lower bounds in both the public and private-coin settings, and a matching upper bound in the public-coin setting. We extend these results, and show unconditional lower bounds for when both classical and quantum communication are permitted. We show the public-coin lower bound is tight by giving an algorithm with a matching upper bound. We also show an almost tight upper bound in the private-coin setting when only quantum communication is permitted.