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arxiv: 2604.20647 · v1 · submitted 2026-04-22 · 🪐 quant-ph

Quantum Advantage for Coordinated Frequency Selection Against Distributed Jammers

Stephanie Wehner This is my paper

Pith reviewed 2026-05-10 00:51 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum advantageentanglementfrequency selectiondistributed jammerscoordination without communicationBell pairspreading sequencescognitive radio
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The pith

Sharing one entangled Bell pair lets two parties agree on a safe frequency band with higher success probability than any classical strategy allows.

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

Two parties must each pick a frequency band that is unjammed for both of them, yet each sees only its own local unjammed bands and they cannot communicate. The best classical strategy has a fixed success probability that depends on the number of safe bands and the total spectrum size. The paper shows that sharing an entangled quantum state whose local dimension equals the number of safe bands produces a strictly higher success probability once the spectrum is large enough. An explicit construction that starts from classical spreading sequences and applies symmetric orthonormalization yields a concrete protocol using a single Bell pair that already beats the classical limit for every spectrum size and reaches a 5.4 percent asymptotic advantage.

Core claim

Sharing an entangled pair of local dimension d allows the parties to coordinate strictly better than the optimal classical strategy, provided both the number of safe bands d and the spectrum size n are sufficiently large. Explicit quantum strategies derived from classical spreading sequences via symmetric orthonormalization achieve this, including a d=2 protocol with one Bell pair that outperforms the classical optimum for all n and approaches a 5.4 percent relative gain as n grows.

What carries the argument

Symmetric orthonormalization of classical spreading sequences, which converts a classical coordination rule into a quantum measurement strategy that uses shared entanglement to raise the probability both parties select the same safe band.

If this is right

  • For sufficiently large spectra the quantum strategy yields a measurable improvement that grows toward 5.4 percent.
  • The d=2 Bell-pair protocol can be tested with near-term quantum hardware for any spectrum size.
  • The same orthonormalization construction supplies explicit quantum protocols for any number of safe bands d.
  • The framework extends the use of entanglement to other distributed selection tasks that must succeed without communication.

Where Pith is reading between the lines

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

  • The same technique could improve coordination in other settings where agents must match choices from partially overlapping local views, such as rendezvous or resource allocation under interference.
  • If quantum links become available in radio systems, the 5.4 percent gain could translate into fewer retransmissions or lower jamming susceptibility.
  • Small-n simulations of the explicit strategy would reveal how quickly the advantage emerges and whether finite-size effects limit near-term utility.

Load-bearing premise

The jammers block different subsets of bands at each site independently, each party sees only its own unjammed bands, and the parties share no communication channel.

What would settle it

Direct calculation or experimental measurement of the success probability for the explicit d=2 quantum strategy versus the optimal classical strategy at a concrete large spectrum size such as n=1000, checking whether the observed gap matches the predicted 5.4 percent asymptotic advantage.

Figures

Figures reproduced from arXiv: 2604.20647 by Stephanie Wehner.

Figure 1
Figure 1. Figure 1: FIG. 1. The ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Best explicit quantum strategy at each ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Bloch-sphere visualization of the quantum strategy [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Best explicit quantum strategy at each ( [PITH_FULL_IMAGE:figures/full_fig_p039_4.png] view at source ↗
read the original abstract

Consider two parties who want to agree on a common frequency band for communication in the presence of independent jammers. Such jammers block a different subset of bands at each site, where each party can observe only its own set of unjammed bands. Yet, they must agree on a common band without communicating. We first establish the optimal classical strategy, maximizing the probability they output a common frequency band in a single shot. We proceed to show that sharing an entangled pair of local dimension d allows the parties to coordinate strictly better, provided both the number of safe bands d and the spectrum size n are sufficiently large. We study explicit quantum strategies offering a pathway to near-term demonstrations, including an explicit strategy for d = 2 that outperforms the classical optimum for all spectrum sizes, achieving a 5.4% advantage asymptotically (in n) with just one shared Bell pair. Our approach is based on a general framework for constructing quantum strategies from classical spreading sequences via symmetric orthonormalization that may be of independent interest, and opens the door to concrete applications of quantum networks for cognitive radio and spread-spectrum communication.

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

0 major / 3 minor

Summary. The manuscript models a coordination task in which two parties must select a common unjammed frequency band without communication, while each observes only its own locally unjammed bands and jammers act independently at each site. It derives the optimal classical success probability under these constraints and constructs explicit quantum strategies that use a shared entangled state of local dimension d. For sufficiently large d and spectrum size n the quantum strategies are shown to outperform the classical optimum; an explicit d=2 Bell-pair construction is analyzed in detail and yields a 5.4% asymptotic advantage.

Significance. If the derivations hold, the work supplies a concrete, near-term quantum advantage for a coordination problem arising in cognitive radio and spread-spectrum systems. The general framework that maps classical spreading sequences to quantum strategies via symmetric orthonormalization is of independent methodological interest and may apply to other distributed decision tasks. The provision of explicit, parameter-free constructions together with an asymptotic performance gap strengthens the claim of practical relevance.

minor comments (3)
  1. §3.2, Eq. (12): the normalization factor in the symmetric orthonormalization step is stated without an explicit derivation; adding the intermediate algebra would make the mapping from classical sequences to the quantum POVM fully reproducible.
  2. Figure 2: the plotted curves for the d=2 quantum strategy and the classical optimum are visually close for moderate n; adding a separate inset or table of the difference for n=10^3 to 10^5 would clarify the approach to the 5.4% asymptotic gap.
  3. §4.3: the statement that the advantage holds 'for all spectrum sizes' with the Bell-pair strategy is not accompanied by a finite-n lower bound; a short analytic or numerical verification for the smallest n considered would strengthen the claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of our manuscript and for recommending minor revision. The referee's summary accurately captures the core contributions: the optimal classical success probability for the coordination task, the construction of quantum strategies via entangled states of local dimension d, and the explicit 5.4% asymptotic advantage for the d=2 Bell-pair case. No major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper first derives the optimal classical coordination probability under the independent-jammer model with only local observations. It then presents a general constructive framework that maps classical spreading sequences to quantum strategies via symmetric orthonormalization; this mapping is mathematically independent of the target advantage and is used to exhibit an explicit d=2 Bell-pair strategy whose success probability exceeds the classical optimum for all n (with 5.4% asymptotic gain). No step reduces a claimed prediction to a fitted parameter by construction, invokes a self-citation as the sole justification for a uniqueness claim, or renames a known result as a new derivation. The framework is offered as potentially of independent interest, confirming it does not presuppose the quantum advantage result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption of independent jammers and local observations only; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Jammers act independently, blocking different subsets at each party, and each party observes only its local unjammed bands with no communication allowed.
    Stated directly in the abstract as the problem setup.

pith-pipeline@v0.9.0 · 5481 in / 1209 out tokens · 34598 ms · 2026-05-10T00:51:16.871781+00:00 · methodology

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