pith. sign in

arxiv: 2604.22804 · v1 · submitted 2026-04-13 · 🪐 quant-ph · cs.IT· math.IT

Deterministic Multi-User Identification over Bosonic Channels

G\"okhan Elmas , Janis N\"otzel This is my paper

Pith reviewed 2026-05-10 15:23 UTC · model grok-4.3

classification 🪐 quant-ph cs.ITmath.IT
keywords bosonic channelsmulti-user identificationcoherent statesquantum identificationmetric entropyphase spacedeterministic identification
0
0 comments X

The pith

Bosonic channels enable deterministic multi-user identification with near-k log k capacity scaling via coherent-state signatures.

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

The paper investigates deterministic identification of multiple users over bosonic channels, which model optical and quantum communication links. Each user receives a unique coherent product state subject to an average energy constraint, and a receiver distinguishes that user through a dedicated binary quantum test. This approach maps users to distinct geometric points in high-dimensional phase space rather than relying on shared classical codebooks. Metric entropy bounds then establish that the identification capacity grows approximately as k log k. A sympathetic reader would care because this scaling suggests quantum optical systems can support far more simultaneous identifications than classical counterparts under comparable resources.

Core claim

Each user is assigned a coherent product state under an average energy constraint, and identification proceeds via a user-specific binary quantum test that places receivers as geometric signatures in high-dimensional phase space. Metric entropy bounds applied to these signatures show that the identification capacity scales as near-k log k.

What carries the argument

Geometric signatures of coherent product states in high-dimensional phase space, distinguished by user-specific binary quantum tests under average energy constraint.

Load-bearing premise

Each user is assigned a distinct coherent product state and identification uses a user-specific binary quantum test that associates receivers with geometric signatures in phase space.

What would settle it

A calculation or experiment demonstrating that the number of reliably identifiable users fails to grow as k log k when coherent states are sent over a bosonic channel under the stated energy constraint and tested with binary measurements.

read the original abstract

We study deterministic multi-user identification over bosonic channels using coherent-state signatures. Each user is assigned a coherent product state under an average energy constraint, and identification is performed by a user-specific binary quantum test. In contrast to classical multi-user identification models based on shared codebooks, this formulation associates each receiver with a geometric signature in high-dimensional phase space. Using metric entropy bounds, we show that the identification capacity exhibits a near-k log k scaling behavior.

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

1 major / 1 minor

Summary. The manuscript studies deterministic multi-user identification over bosonic channels. Each of the k users is assigned a coherent product state satisfying an average energy constraint; identification proceeds via a user-specific binary quantum test that exploits the geometric signature of the state in high-dimensional phase space. The central claim is that metric-entropy bounds on these signatures imply an identification capacity that scales as approximately k log k.

Significance. If the claimed scaling is established with a complete error analysis, the result would extend classical identification-capacity techniques to continuous-variable quantum channels and supply a concrete scaling law useful for quantum network design. The approach of mapping coherent-state assignments to phase-space signatures and invoking metric entropy is technically interesting and, if the quantum-to-classical gap is closed, would constitute a clear contribution.

major comments (1)
  1. [proof of the main scaling result (application of metric entropy bounds)] The derivation that applies metric entropy bounds to the set of coherent-product-state signatures (the step that produces the near-k log k scaling) does not supply an explicit relation between the classical covering radius ε and the minimum phase-space distance d required to keep the Helstrom error probability of each binary test below a fixed threshold. Because coherent states are non-orthogonal, the binary-test error is (1 − √(1 − exp(−d²)))/2; without a quantitative link between ε and d under the average-energy constraint, it is unclear whether the metric-entropy covering number directly controls the quantum identification error and therefore whether the stated scaling follows.
minor comments (1)
  1. [abstract] The abstract states the scaling result but does not indicate whether the bound is of the form (1−o(1))k log k or contains additional logarithmic or constant factors; a precise statement would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comment on the proof of the main scaling result. We address the point below.

read point-by-point responses

  1. Referee: The derivation that applies metric entropy bounds to the set of coherent-product-state signatures (the step that produces the near-k log k scaling) does not supply an explicit relation between the classical covering radius ε and the minimum phase-space distance d required to keep the Helstrom error probability of each binary test below a fixed threshold. Because coherent states are non-orthogonal, the binary-test error is (1 − √(1 − exp(−d²)))/2; without a quantitative link between ε and d under the average-energy constraint, it is unclear whether the metric-entropy covering number directly controls the quantum identification error and therefore whether the stated scaling follows.

    Authors: We agree that an explicit quantitative link between the covering radius ε and the minimum phase-space distance d is required to rigorously bound the Helstrom error of each binary test. In the revised manuscript we will insert a new lemma establishing this relation under the average-energy constraint. For coherent-product states the phase-space Euclidean distance d between distinct signatures satisfies d ≥ 2ε (by definition of a minimal covering), which directly controls the overlap and hence the Helstrom error probability (1 − √(1 − exp(−d²)))/2. Choosing ε small enough but independent of k (e.g., ε = Θ(1/√k) or smaller) keeps every binary-test error below any fixed threshold while preserving the leading k log k term in the metric-entropy bound; the additional log(1/ε) factor is only O(log k) and does not alter the claimed scaling. The revised text will also verify compatibility with the average-energy constraint. revision: yes

Circularity Check

0 steps flagged

No significant circularity; scaling follows from external metric entropy bounds on phase-space signatures

full rationale

The paper's central derivation applies standard metric entropy bounds to the geometric signatures of coherent product states under average energy constraint to obtain the near-k log k identification capacity scaling. No equations, parameters, or self-citations are shown reducing this scaling to a fitted input, self-defined quantity, or prior author result by construction. The binary quantum tests and phase-space geometry are defined independently of the final scaling claim, making the argument self-contained against external benchmarks rather than internally circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into parameters and axioms; the central claim appears to rest on standard quantum mechanics and metric entropy bounds from information theory.

axioms (2)
  • domain assumption Bosonic channels admit coherent product states under average energy constraint
    Stated directly in the abstract as the assignment method for user signatures.
  • standard math Metric entropy bounds apply to the geometric signatures in high-dimensional phase space
    Invoked to derive the scaling behavior.

pith-pipeline@v0.9.0 · 5363 in / 1229 out tokens · 21218 ms · 2026-05-10T15:23:02.422032+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages

  1. [1]

    Identification in the presence of feedback: A discovery of new capacity formulas.IEEE Transactions on Information Theory, 35(1):30–36, January 1989

    Rudolf Ahlswede and Gunter Dueck. Identification in the presence of feedback: A discovery of new capacity formulas.IEEE Transactions on Information Theory, 35(1):30–36, January 1989

    work page 1989

  2. [2]

    Identification via channels.IEEE Transactions on Information Theory, 35(1):15–29, January 1989

    Rudolf Ahlswede and Gunter Dueck. Identification via channels.IEEE Transactions on Information Theory, 35(1):15–29, January 1989

    work page 1989

  3. [3]

    Quantum limits in optical communications.Journal of Lightwave Technology, 38(10):2741–2754, May 2020

    Konrad Banaszek, Ludwig Kunz, Michal Jachura, and Marcin Jarzyna. Quantum limits in optical communications.Journal of Lightwave Technology, 38(10):2741–2754, May 2020

    work page 2020

  4. [4]

    Secure and robust identification via classical-quantum channels.IEEE Transactions on Information Theory, 65(10):6734–6749, October 2019

    Holger Boche, Christian Deppe, and Andreas Winter. Secure and robust identification via classical-quantum channels.IEEE Transactions on Information Theory, 65(10):6734–6749, October 2019

    work page 2019

  5. [5]

    Mross, Yaning Zhao, Wafa Labidi, Christian Deppe, and Eduard A

    Larissa Brüche, Marcel A. Mross, Yaning Zhao, Wafa Labidi, Christian Deppe, and Eduard A. Jorswieck. Converse techniques for identification via channels, 2024

    work page 2024

  6. [6]

    De- terministic identification over channels with finite output: A dimensional perspective on superlinear rates.IEEE Transactions on Information Theory, 71(5):3373–3396, May 2025

    Pau Colomer, Christian Deppe, Holger Boche, and Andreas Winter. De- terministic identification over channels with finite output: A dimensional perspective on superlinear rates.IEEE Transactions on Information Theory, 71(5):3373–3396, May 2025

    work page 2025

  7. [7]

    Rate-reliability tradeoff for deterministic identification over gaussian channels, 2026

    Pau Colomer, Christian Deppe, Holger Boche, and Andreas Winter. Rate-reliability tradeoff for deterministic identification over gaussian channels, 2026

    work page 2026

  8. [8]

    New results in the theory of identification via channels.IEEE Transactions on Information Theory, 38(1):14–25, January 1992

    Te Sun Han and Sergio Verdú. New results in the theory of identification via channels.IEEE Transactions on Information Theory, 38(1):14–25, January 1992

    work page 1992

  9. [9]

    M. Hayashi. General nonasymptotic and asymptotic formulas in channel resolvability and identification capacity and their application to the wiretap channel.IEEE Transactions on Information Theory, 52(4):1562– 1575, 2006

    work page 2006

  10. [10]

    Weak decoupling duality and quantum identification.IEEE Transactions on Information Theory, 58(7):4914–4929, 2012

    Patrick Hayden and Andreas Winter. Weak decoupling duality and quantum identification.IEEE Transactions on Information Theory, 58(7):4914–4929, 2012

    work page 2012

  11. [11]

    Holevo.Quantum Systems, Channels, Information: A Mathematical Introduction

    Alexander S. Holevo.Quantum Systems, Channels, Information: A Mathematical Introduction. De Gruyter, Berlin/Boston, 2012

    work page 2012

  12. [12]

    Springer, 2023

    Chon-Fai Kam, Wei-Min Zhang, and Da-Hsuan Feng.Coherent States: New Insights into Quantum Mechanics with Applications, volume 1011 ofLecture Notes in Physics. Springer, 2023

    work page 2023

  13. [13]

    Paulina Marian and Tudor A. Marian. Optimal purifications and fidelity for displaced thermal states.Physical Review A, 76(5), November 2007

    work page 2007

  14. [14]

    Identification over quantum broadcast channels.Quantum Information Processing, 22(10):361, 2023

    Johannes Rosenberger, Christian Deppe, and Uzi Pereg. Identification over quantum broadcast channels.Quantum Information Processing, 22(10):361, 2023

    work page 2023

  15. [15]

    Identification over compound multiple-input multiple-output broadcast channels.IEEE Transactions on Information Theory, 69(7):4178–4195, 2023

    Johannes Rosenberger, Uzi Pereg, and Christian Deppe. Identification over compound multiple-input multiple-output broadcast channels.IEEE Transactions on Information Theory, 69(7):4178–4195, 2023

    work page 2023

  16. [16]

    Salariseddigh, Uzi Pereg, Holger Boche, and Christian Deppe

    Mohammad J. Salariseddigh, Uzi Pereg, Holger Boche, and Christian Deppe. Deterministic identification over channels with power con- straints.IEEE Transactions on Information Theory, 68(1):1–24, 2022

    work page 2022

  17. [17]

    Mohammad Javad Salariseddigh, Vahid Jamali, Uzi Pereg, Holger Boche, Christian Deppe, and Robert Schober. Deterministic identifi- cation for molecular communications over the poisson channel.IEEE Transactions on Molecular, Biological, and Multi-Scale Communica- tions, 9(4):408–424, 2023

    work page 2023

  18. [18]

    CRC Press, Boca Raton, 2017

    Alessio Serafini.Quantum Continuous Variables: A Primer of Theoret- ical Methods. CRC Press, Boca Raton, 2017

    work page 2017

  19. [19]

    Stanisław J. Szarek. Metric entropy of homogeneous spaces.Banach Center Publications, 43(1):395–410, 1998

    work page 1998

  20. [20]

    Cerf, Timothy C

    Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J. Cerf, Timothy C. Ralph, Jeffrey H. Shapiro, and Seth Lloyd. Gaussian quantum information.Reviews of Modern Physics, 84(2):621–669, 2012

    work page 2012

  21. [21]

    Quantum and classical message identification via quan- tum channels.Quantum Information and Computation, 4(6&7):563–578, 2004

    Andreas Winter. Quantum and classical message identification via quan- tum channels.Quantum Information and Computation, 4(6&7):563–578, 2004

    work page 2004

  22. [22]

    Identification via quantum channels in the presence of prior correlation and feedback

    Andreas Winter. Identification via quantum channels in the presence of prior correlation and feedback. InGeneral Theory of Information Transfer and Combinatorics, volume 4123 ofLecture Notes in Computer Science, pages 486–504. Springer, 2006

    work page 2006