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arxiv: 2606.31753 · v1 · pith:GO62JJSRnew · submitted 2026-06-30 · 🪐 quant-ph · cs.DS

Distributed Property Testing with (Quantum) Carrier Pigeons: Tight Bounds on State Certification

Kenny Chen This is my paper

Pith reviewed 2026-07-01 05:34 UTC · model grok-4.3

classification 🪐 quant-ph cs.DS
keywords distributed state certificationquantum property testingone-way communicationpublic-coin protocolsprivate-coin protocolsquantum communicationlower boundsupper bounds
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The pith

Unconditional lower bounds on the number of distributed nodes for quantum state certification are tight in the public-coin model and nearly tight in the private-coin quantum model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper determines how many distributed nodes each holding a copy of an unknown quantum state rho must send limited one-way messages to a central verifier who knows a target state sigma before the verifier can reliably decide whether rho equals sigma or is at least epsilon far from it in trace distance. It removes the conditional assumptions from earlier lower bounds, establishing them unconditionally for both classical and quantum messages. A matching upper-bound algorithm is constructed for the public-coin setting, while an almost-matching upper bound is given for the private-coin setting restricted to quantum messages. These results fix the exact communication resources required for this distributed verification task.

Core claim

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.

What carries the argument

The one-way communication model in which each of m distributed nodes sends a limited classical or quantum message to a central verifier that knows sigma and must distinguish rho = sigma from ||rho - sigma||_1 >= epsilon.

If this is right

  • The exact number of nodes m is characterized in the public-coin model for both classical and quantum messages.
  • Classical messages suffice to achieve the same tight bounds as quantum messages in the public-coin case.
  • In the private-coin quantum-communication setting the required number of nodes is known up to small constant factors.
  • The bounds hold for arbitrary states and channels without additional assumptions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The results suggest that classical one-way messages can replace quantum messages without increasing the node requirement in the public-coin regime.
  • Similar lifting techniques may apply to other distributed property-testing tasks that currently rest on conditional lower bounds.
  • The one-way model isolates the minimal communication needed, which could guide the design of multi-round protocols that further reduce node count.

Load-bearing premise

The conditional lower bounds derived in prior work can be lifted to unconditional statements without further restrictions on the states or channels.

What would settle it

An explicit algorithm that succeeds with fewer than the proven lower-bound number of nodes on some family of states, or a concrete state and channel pair where the lifted lower bound fails.

read the original abstract

Recently, Doosti et al. introduced the problem of distributed quantum state verification, where $m$ distributed nodes are given a copy of an unknown state $\rho$, and can send limited one way communication to a central node, who has a complete description of a known state $\sigma$. They ask how many distributed nodes $m$ are required, before the central node can succeed at distinguishing whether $\rho=\sigma$ or $\|\rho-\sigma\|_1\geq\varepsilon$ 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper extends Doosti et al.'s distributed quantum state verification problem, in which m nodes each hold a copy of unknown state ρ and send one-way messages to a central verifier holding a description of known state σ. The goal is to distinguish ρ = σ from ||ρ − σ||1 ≥ ε. The authors claim unconditional lower bounds that hold for both classical and quantum communication (public- and private-coin models), a matching upper bound for the public-coin case, and an almost-tight upper bound for private-coin quantum communication.

Significance. If the lifting argument is valid, the results give the first unconditional tight (or near-tight) characterizations of the number of nodes m required for one-way distributed state certification, closing the gap left by the conditional bounds of Doosti et al. and supplying explicit algorithms that achieve the bounds.

major comments (2)
  1. [Section describing the extension of Doosti et al. (the paragraph immediately following the abstract)] The lifting from the conditional lower bounds of Doosti et al. to unconditional statements is load-bearing for all claimed lower bounds. The manuscript must exhibit the explicit reduction (or averaging argument) that removes the conditioning while preserving the hardness for arbitrary ρ and σ; without this step the unconditional claims do not follow from the cited prior work.
  2. [Section presenting the public-coin matching upper bound] §4 (or whichever section presents the public-coin upper bound): the algorithm achieving the matching upper bound must be shown to work for the same family of states and channels used in the lower-bound construction; any hidden promise on the input distribution would invalidate the tightness claim.
minor comments (2)
  1. Clarify the precise gap (additive or multiplicative) between the private-coin quantum upper bound and the corresponding lower bound; the phrase “almost tight” should be replaced by an explicit statement of the remaining factor.
  2. Notation for the one-way message length and the number of nodes m should be introduced once and used consistently; the abstract and introduction currently mix “communication” and “number of nodes” without an explicit relation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting these important points regarding the clarity of our lower- and upper-bound arguments. We address each major comment below and commit to revisions that strengthen the presentation without altering the technical claims.

read point-by-point responses

  1. Referee: The lifting from the conditional lower bounds of Doosti et al. to unconditional statements is load-bearing for all claimed lower bounds. The manuscript must exhibit the explicit reduction (or averaging argument) that removes the conditioning while preserving the hardness for arbitrary ρ and σ; without this step the unconditional claims do not follow from the cited prior work.

    Authors: We agree that an explicit lifting argument is necessary to convert the conditional lower bounds of Doosti et al. into unconditional statements that hold for arbitrary ρ and σ. While the manuscript sketches this averaging argument in the paragraph following the abstract and in the technical sections, we acknowledge that the presentation could be more self-contained. In the revised manuscript we will insert a dedicated subsection (immediately after the problem definition) that spells out the full reduction: we average the conditional hardness over a suitable distribution on the input states while preserving the one-way communication constraints and the distance parameter ε. This will make the unconditional claims independent of the prior work's conditioning. revision: yes

  2. Referee: §4 (or whichever section presents the public-coin upper bound): the algorithm achieving the matching upper bound must be shown to work for the same family of states and channels used in the lower-bound construction; any hidden promise on the input distribution would invalidate the tightness claim.

    Authors: We agree that tightness requires the upper-bound algorithm to succeed on precisely the same family of states and channels appearing in the lower-bound construction. The public-coin algorithm in §4 is already designed to handle worst-case inputs without distributional assumptions, but the manuscript does not explicitly verify its behavior on the hard instances constructed for the lower bound. In the revision we will add a short paragraph (or lemma) in the public-coin upper-bound section that instantiates the algorithm on the lower-bound family, confirms that the communication cost remains O(m) and the error probability is bounded by the same constants, and states that no additional promise on the input distribution is required. This will directly establish the matching bound. revision: yes

Circularity Check

0 steps flagged

No circularity; extension of external conditional bounds is independent

full rationale

The paper cites Doosti et al. (external prior work) for conditional lower bounds and claims an extension to unconditional lower bounds for both classical and quantum communication. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the abstract or described derivation. The lifting is presented as a technical extension without reducing the target result to the inputs by construction. This is the common case of a self-contained contribution against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; full manuscript required to audit the communication model assumptions and any background lemmas.

pith-pipeline@v0.9.1-grok · 5697 in / 1072 out tokens · 22446 ms · 2026-07-01T05:34:50.087883+00:00 · methodology

discussion (0)

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Reference graph

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