pith. sign in

arxiv: 2604.08241 · v1 · submitted 2026-04-09 · 🪐 quant-ph

Evaluating the performance of a weak-field homodyne receiver in quadrature phase-shift keying optical communication

Silvia Cassina , Alex Pozzoli , Michele N. Notarnicola , Marco Lamperti , Stefano Olivares , Alessia Allevi This is my paper

Pith reviewed 2026-05-10 16:50 UTC · model grok-4.3

classification 🪐 quant-ph
keywords weak-field homodynequadrature phase-shift keyingcoherent statesmutual informationsecret key ratequantum communicationphase noise feedbackoptical detection
0
0 comments X

The pith

Weak-field homodyne receivers blend wave and particle features to serve as a practical alternative to standard optical homodyne detection in phase-encoded communication.

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

The paper tests whether a weak-field receiver can match conventional homodyne performance when transmitting information via coherent states that share the same amplitude but carry one of four distinct phases. A feedback loop stabilizes the phase reference so the four states remain distinguishable at the receiver. Measured mutual information and secret-key rates remain competitive with ideal homodyne detection, showing that the hybrid detection scheme extracts useful information without requiring full-strength local-oscillator fields. These results are presented as evidence that the receiver concept is ready for scaling toward larger alphabets that approach continuous phase modulation.

Core claim

We have demonstrated that weak-field receivers, merging wave-like and particle-like features, can be considered as a valid alternative to already existing receivers, such as optical homodyne detection. To better emphasize the potential of our receiver, in this work we consider a proof of concept for quaternary communication based on coherent states with the same amplitude and different phase values. The encoding in phase requires a fine control of phase noise obtained through a feedback system. The results achieved in terms of mutual information and secret key generation rate encourage further increase of the alphabet towards an approximately continuous phase modulation.

What carries the argument

The weak-field homodyne receiver that combines continuous wave-like field detection with discrete particle-like photon counting to decode phase shifts among equal-amplitude coherent states.

If this is right

  • Quaternary phase encoding becomes feasible once the feedback loop suppresses phase fluctuations to the required level.
  • Mutual information extracted from the four states approaches the theoretical limit set by homodyne detection.
  • Secret-key rates remain positive, indicating the scheme can support secure quantum communication links.
  • Performance trends support extension to larger phase alphabets that approach continuous modulation.

Where Pith is reading between the lines

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

  • The same receiver architecture might be adapted to other discrete modulation formats without redesigning the optical front end.
  • Integration with existing fiber links could be simpler than full homodyne systems because lower local-oscillator power is needed.
  • If phase stabilization scales with alphabet size, the approach could reduce the hardware overhead for continuous-variable quantum key distribution.
  • Laboratory demonstrations with higher mean photon numbers would test whether the advantage persists outside the weak-field regime.

Load-bearing premise

The feedback system provides sufficient phase-noise suppression for reliable encoding and decoding of the four phase values in the experimental or simulated setup.

What would settle it

A side-by-side measurement in which the weak-field receiver yields a mutual information value at least 10 percent lower than the ideal homodyne benchmark at the same mean photon number would falsify the claim of comparable performance.

Figures

Figures reproduced from arXiv: 2604.08241 by Alessia Allevi, Alex Pozzoli, Marco Lamperti, Michele N. Notarnicola, Silvia Cassina, Stefano Olivares.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the QPSK constellation analyzed in this work, with the reference phase [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Mutual information as a function of the losses affecting the signal arm in the case of WF receiver (solid curves) and [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Sketch of the experimental setup. BS: beam splitter, VND: variable neutral density filter, M: mirror, SiPM: Silicon [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Temporal trace of the extracted phase in two conditions: (a) unlocked interferometer with box open; (b) fast lock [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Graph of the overlapping Allan deviation curves for the four operating conditions: blue, lock off and box open; red, [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Graph of the ASD for three operating conditions: blue, lock off and box open; green, lock on and box open; purple, [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Photon-number difference for detected photons in the cases of [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Photon-number difference for detected photons in the case of the QPSK encoding for two different choices of the mean [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Mutual information as a function of the losses affecting the signal for BPSK (green) and QPSK (blue) encodings. Dots: [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. KGR as a function of the losses on the signal for BPSK (green curve) and QPSK (blue curve) modulation. The KGR [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

Quantum communication protocols require efficient detection schemes to maximize the information transfer rate between the sender and the receiver. To this aim, we have demonstrated that weak-field receivers, merging wave-like and particle-like features, can be considered as a valid alternative to already existing receivers, such as optical homodyne detection. To better emphasize the potential of our receiver, in this work we consider a proof of concept for quaternary communication based on coherent states with the same amplitude and different phase values. The encoding in phase requires a fine control of phase noise obtained through a feedback system. The results achieved in terms of mutual information and secret key generation rate encourage further increase of the alphabet towards an approximately continuous phase modulation.

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 presents a proof-of-concept for a weak-field homodyne receiver applied to quaternary phase-shift keying (QPSK) communication with coherent states of fixed amplitude but four distinct phases. It highlights the merging of wave-like and particle-like detection features and argues that the scheme constitutes a valid alternative to conventional optical homodyne receivers, supported by reported values of mutual information and secret-key generation rate. Phase encoding is stated to require active feedback for phase-noise control.

Significance. If the quantitative results on mutual information and secret-key rate are shown to exceed or match the homodyne benchmark under properly quantified residual phase noise, the work would offer a concrete experimental route toward hybrid detection schemes that could improve information rates in quantum optical links. The explicit use of feedback-stabilized phase encoding and the focus on finite-alphabet coherent-state communication provide a falsifiable test of the receiver's practicality.

major comments (1)
  1. [Abstract and §3] Abstract and §3 (experimental setup): the central claim that the weak-field receiver is a 'valid alternative' to standard homodyne detection rests entirely on the reported mutual-information and secret-key-rate figures, yet no measured residual phase variance, loop bandwidth, or resulting symbol-error probability is supplied. In the shot-noise-limited weak-field regime any uncorrected phase jitter directly mixes the I and Q quadratures, so the unquantified performance of the feedback loop is load-bearing for the distinguishability of the four equiphase states.
minor comments (1)
  1. [Introduction] Notation for the four phase states and the definition of the weak-field regime should be introduced with explicit equations rather than descriptive text only.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments correctly identify the need for explicit characterization of the phase-stabilization loop to support claims about the weak-field receiver's performance relative to standard homodyne detection. We have revised the manuscript to incorporate the requested quantitative details from our experimental data.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (experimental setup): the central claim that the weak-field receiver is a 'valid alternative' to standard homodyne detection rests entirely on the reported mutual-information and secret-key-rate figures, yet no measured residual phase variance, loop bandwidth, or resulting symbol-error probability is supplied. In the shot-noise-limited weak-field regime any uncorrected phase jitter directly mixes the I and Q quadratures, so the unquantified performance of the feedback loop is load-bearing for the distinguishability of the four equiphase states.

    Authors: We agree that the performance of the active phase-noise feedback must be quantified to substantiate the distinguishability of the four equiphase states and the validity of the weak-field receiver as an alternative. The reported mutual-information and secret-key-rate values were computed directly from the experimentally recorded quadrature samples; any residual phase jitter is therefore already embedded in those figures. To address the referee's concern explicitly, we have added to the revised Section 3 (and a new supplementary figure) the measured residual phase variance extracted from the feedback error signal, the servo loop bandwidth, and the symbol-error probability inferred from the observed quadrature histograms. These additions confirm that phase jitter remains low enough to avoid significant I-Q mixing, thereby reinforcing that the achieved rates are obtained under well-controlled phase encoding. revision: yes

Circularity Check

0 steps flagged

No circularity: results rest on external experimental validation rather than self-referential definitions or fits

full rationale

The paper reports measured or simulated mutual information and secret-key rates for a weak-field homodyne receiver applied to QPSK coherent states, positioning the scheme as an alternative to standard homodyne detection. No equations are presented that define a quantity in terms of itself (e.g., no per-period scale fitted from data then re-used as a prediction of the same ratio). The feedback loop for phase-noise control is stated as a prerequisite but is not derived from the reported rates; the rates themselves are the output of the setup rather than inputs that force the conclusion. Self-citations, if present, are not load-bearing for the central performance claim, which is supported by direct comparison to homodyne benchmarks outside the derivation. The chain therefore remains non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the central claim rests on an experimental demonstration whose details are not visible.

pith-pipeline@v0.9.0 · 5431 in / 1008 out tokens · 36349 ms · 2026-05-10T16:50:00.710827+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

43 extracted references · 43 canonical work pages

  1. [1]

    Cariolaro G 2015Quantum Communications(Springer International Publishing)

    work page

  2. [2]

    Flamini F, Spagnolo N and Sciarrino F 2019 Photonic quantum information processing: a reviewRep. Prog. Phys.82 016001

    work page 2019

  3. [3]

    Quantum Technol.21970073

    Cozzolino D, Da Lio B, Bacco D and Oxenløwe L K 2019 High-Dimensional Quantum Communication: Benefits, Progress, and Future ChallengesAdv. Quantum Technol.21970073

    work page 2019

  4. [4]

    Arrazola J M and L¨ utkenhaus N 2014 Quantum communication with coherent states and linear opticsPhys. Rev. A90 042335

    work page 2014

  5. [5]

    Arrazola J M and Karasamanis M and L¨ utkenhaus N 2016 Practical quantum retrieval gamesPhys. Rev. A93062311

    work page 2016

  6. [6]

    DiMario M T, Kunz L, Banaszek K and Becerra F E 2019 Optimized communication strategies with binary coherent states over phase noise channelsnpj Quantum Inf.565

    work page 2019

  7. [7]

    Grosshans F and Grangier P 2002 Continuous Variable Quantum Cryptography Using Coherent StatesPhys. Rev. Lett. 88057902

    work page 2002

  8. [8]

    Diamanti E, Lo H-K, Qi B and Yuan Z 2016 Practical challenges in quantum key distributionnpj Quantum Inf.216025

    work page 2016

  9. [9]

    Cattaneo M, Paris M G A and Olivares S 2018 Hybrid quantum key distribution using coherent states and photon-number- resolving detectorsPhys. Rev. A98012333

    work page 2018

  10. [10]

    Express32, 39846-39859

    Sanvito A, Cassina S, Lamperti M, Notarnicola M N, Olivares S and Allevi A (2024) Assessing a binary quantum channel exploiting a Silicon photomultiplier based hybrid receiverOpt. Express32, 39846-39859

    work page 2024

  11. [11]

    Mazzocchi A, Notarnicola M N, Cassina S, Lamperti M, Olivares S and Allevi A (2025) Implementation of a hybrid SiPM receiver for applications to continuous-variable quantum key distribution with binary modulationInt. J. Quantum Inform. -, 2540011

    work page 2025

  12. [12]

    Izumi S, Takeoka M, Fujiwara M, Dalla Pozza N, Assalini A, Ema K and Sasaki M 2012 Displacement receiver for phase- shift-keyed coherent statesPhys. Rev. A86042328

    work page 2012

  13. [13]

    Phys.17032003

    M¨ uller C R and Marquardt Ch 2015 A robust quantum receiver for phase shift keyed signalsNew J. Phys.17032003

    work page 2015

  14. [14]

    Express2510685-10692

    Bina M, Allevi A, Bondani M and Olivares S 2017 Homodyne-like detection for coherent state-discrimination in the presence of phase noiseOpt. Express2510685-10692

    work page 2017

  15. [15]

    Commun.72375-386

    Notarnicola M N, Olivares S, Forestieri E, Parente E, Pot` ı L and Secondini M 2024 Probabilistic Amplitude Shaping for Continuous-Variable Quantum Key Distribution With Discrete Modulation Over a Wiretap ChannelIEEE Trans. Commun.72375-386

    work page 2024

  16. [16]

    Parente E, Notarnicola M N, Olivares S, Forestieri E, Pot` ı L and Secondini M 2026 Discrete-modulation continuous-variable quantum key distribution with probabilistic amplitude shaping over a linear quantum channel arXiv:2603.02870 [quant-ph]

    work page arXiv 2026

  17. [17]

    Leverrier A and Grangier P 2009 Unconditional security proof of long-distance continuous-variable quantum key distribu- tion with discrete modulationPhys. Rev. Lett.102180504

    work page 2009

  18. [18]

    Technol.2, 024010

    Hirano T, Ichikawa T, Matsubara T, Ono M, Oguri Y, Namiki R, Kasai K, Matsumoto R and Tsurumaruand T 2017 Implementation of continuous-variable quantum key distribution with discrete modulationQuantum Sci. Technol.2, 024010

    work page 2017

  19. [19]

    Ghorai S, Grangier P, Diamanti E and Leverrier A 2019 Asymptotic Security of Continuous-Variable Quantum Key Distribution with a Discrete ModulationPhys. Rev. X9021059

    work page 2019

  20. [20]

    Kunz L, DiMario M T, Becerra F E and Banaszek K 2019 Beating the Standard Quantum Limit for Binary Constellations in the Presence of Phase Noise in21st International Conference on Transparent Optical Networks (ICTON), Angers, France

    work page 2019

  21. [21]

    Notarnicola M N and Olivares S 2025 Employing Weak-Field Homodyne Detection for Optical CommunicationsIEEE J. Sel. Areas Commun.431524-1535

    work page 2025

  22. [22]

    Commun.42028

    Becerra F E, Fan J and Migdall A 2013 Implementation of generalized quantum measurements for unambiguous discrimi- nation of multiple non-orthogonal coherent statesNat. Commun.42028

    work page 2013

  23. [23]

    Photonics7147–152

    Becerra F E, Fan J, Baumgartner G, Goldhar J, Kosloski J T and Migdall A 2013 Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discriminationNat. Photonics7147–152

    work page 2013

  24. [24]

    Lightwave Technol.382741-2754

    Banaszek K, Kunz L, Jachura M and Jarzyna M 2020 Quantum Limits in Optical CommunicationsIEEE J. Lightwave Technol.382741-2754

    work page 2020

  25. [25]

    Phys.12 053019

    Sych D and Leuchs G 2010 Coherent state quantum key distribution with multi letter phase-shift keyingNew J. Phys.12 053019

    work page 2010

  26. [26]

    Lett.441371-1374

    Chesi G, Malinverno L, Allevi A, Santoro R, Caccia M and Bondani M 2019 Measuring nonclassicality with silicon photomultipliersOpt. Lett.441371-1374

    work page 2019

  27. [27]

    Cassina S, Allevi A, Mascagna V, Prest M, Vallazza E and Bondani M 2021 Exploiting the wide dynamic range of silicon photomultipliers for quantum optics applicationsEPJ Quantum Technol.84

    work page 2021

  28. [28]

    Commun.613362-3373

    H¨ ager C, Graell i Amat A, Alvarado A and Agrell E 2013 Design of APSK constellations for coherent optical channels with nonlinear phase noiseIEEE Trans. Commun.613362-3373

    work page 2013

  29. [29]

    Commun.22168-180 13

    Thomas C M, Weidner M Y and Durrani S H 1974 Digital amplitude-phase keying with M-ary alphabetsIEEE Trans. Commun.22168-180 13

    work page 1974

  30. [30]

    Commun.32616-626

    Biglieri E 1984 High-level modulation and coding for nonlinear satellite channels,IEEE Trans. Commun.32616-626

    work page 1984

  31. [31]

    Wireless Commun.52396-2407

    De Gaudenzi R, Guill´ en i F` abregas A and Martinez A 2006 Performance analysis of turbo-coded APSK modulations over nonlinear satellite channelsIEEE Trans. Wireless Commun.52396-2407

    work page 2006

  32. [32]

    Sung W, Kang S, Kim P, Chang D I and Shin D J 2009 Performance analysis of APSK modulation for DVB-S2 transmission over nonlinear channelsInt. J. Commun. Syst. Network27295-311

    work page 2009

  33. [33]

    Notarnicola M N 2025 Quantum communications in continuous variable systemsInt. J. Quantum Inf.232550003

    work page 2025

  34. [34]

    Cover T M 1999Elements of information theory(John Wiley & Sons)

    work page

  35. [35]

    Lightwave Technol.292790-2800

    Colavolpe G, Foggi T, Forestieri E and Secondini M 2011 Impact of Phase Noise and Compensation Techniques in Coherent Optical SystemsJ. Lightwave Technol.292790-2800

    work page 2011

  36. [36]

    https:// pyrpl.readthedocs.io/en/latest/

    work page

  37. [37]

    Neuhaus L, Metzdorff R, Chua S, Jacqmin T, Briant T, Heidmann A, Cohadon P-F, Deleglise S 2017 PyRPL (Python Red Pitaya Lockbox) — An open-source software package for FPGA-controlled quantum optics experimentsConference on Lasers and Electro-Optics Europe&European Quantum Electronics Conference (CLEO/Europe-EQEC), Munich, Germany 1-1

    work page 2017

  38. [38]

    Express3351351-51361

    Cassina S, Pozzoli A and Allevi A 2025 Statistical characterization of discrete amplitude-modulated coherent states at telecom wavelengths by means of an up-conversion-based photon-number-resolving detectorOpt. Express3351351-51361

    work page 2025

  39. [39]

    Riley W J 2008 Handbook of frequency stability analysisNatl. Inst. Stand. Technol. Spec. Publ.1065

    work page 2008

  40. [40]

    Bondani M, Allevi A, Agliati A and Andreoni A 2009 Self-consistent characterization of light statisticsJ. Mod. Opt.56 226-231

    work page 2009

  41. [41]

    Cassina S, Notarnicola M N, Olivares S and Allevi A 2025 On the application of a Silicon photomultiplier-based receiver for binary phase-shift-keying protocolsPhys. Lett. A541130403

    work page 2025

  42. [42]

    Express307501–7510

    Lin J, Sun Y, Wu W, Huang K, Liang Y, Yan M and Zeng H 2022 High-speed photon-number-resolving detection via a GHz-gated SiPMOpt. Express307501–7510

    work page 2022

  43. [43]

    Photonics8016009

    Peri A, Gualandi G, Bertapelle T, Sabatini M, Corrielli G, Pi´ etri Y, Marangon D G, Vallone G, Villoresi P, Osellame R and Avesani M 2026 High-performance heterodyne receiver for quantum information processing in a laser written integrated photonic platformAdv. Photonics8016009

    work page 2026