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arxiv: 2510.16204 · v1 · submitted 2025-10-17 · 🪐 quant-ph · cond-mat.dis-nn· physics.optics

Decoherence-free subspaces in the noisy dynamics of discrete-step quantum walks in a photonic lattice

Rajesh Asapanna , Cl\'ement Hainaut , Alberto Amo , \'Alvaro G\'omez-Le\'on This is my paper

Pith reviewed 2026-05-18 05:42 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nnphysics.optics
keywords quantum walksdecoherence-free subspacesphotonic latticeFloquet systemstopological statestemporal noisemaster equationbulk states
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The pith

Certain bulk states in quantum walks stay coherent under constant noise while topological edge states decohere.

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

This paper explores the impact of different temporal noise types on discrete-step quantum walks in a photonic lattice. It finds that noise constant within each Floquet period creates decoherence-free momentum subspaces in the bulk. Fully random noise leads to fast decoherence, and topological edge states decohere for all noise types. The authors derive a non-perturbative master equation to explain this and confirm it with an experiment in a double-fibre ring setup. The surprising result is that bulk states can be more robust to this noise than topological edge states.

Core claim

We find that in the bulk, temporal noise that is constant within a Floquet period leads to decoherence-free momentum subspaces, whereas fully random noise destroys coherence in a few time-steps. When considering topological edge states, we observe decoherence no matter the type of temporal noise. To explain these results, we derive a non-perturbative master equation to describe the system's dynamics and experimentally confirm our findings in a discrete mesh photonic lattice implemented in a double-fibre ring setup.

What carries the argument

Decoherence-free momentum subspaces in the bulk for noise constant within Floquet periods; this mechanism allows unitary evolution in those subspaces despite the noise.

If this is right

  • The bulk can host more robust states than topological edges under correlated temporal noise.
  • Non-perturbative methods are necessary to capture the exact dynamics of this system.
  • Photonic implementations allow direct observation of these protected subspaces.

Where Pith is reading between the lines

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

  • Designers of quantum devices might prefer bulk states over edge states for noise resilience in periodically driven systems.
  • Similar effects may appear in other periodically driven quantum systems beyond walks.
  • Experimentally varying the noise correlation time could map out the boundary of the decoherence-free regime.

Load-bearing premise

The noise stays constant during each entire Floquet period rather than fluctuating within it.

What would settle it

If bulk momentum states lose coherence as quickly as edge states even when noise is held constant within periods, that would contradict the claim.

Figures

Figures reproduced from arXiv: 2510.16204 by Alberto Amo, \'Alvaro G\'omez-Le\'on, Cl\'ement Hainaut, Rajesh Asapanna.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Scheme of the experimental setup with beam [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Measured light intensity in the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Measured dispersions under different types of noise [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Measured (dots) averaged occupation probability [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Zoom on the first time steps of the measured time [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Numerically computed edge state return probability [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Two-dimensional Fourier transform (2D-FT) of [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

We study the noisy dynamics of periodically driven, discrete-step quantum walks in a one-dimensional photonic lattice. We find that in the bulk, temporal noise that is constant within a Floquet period leads to decoherence-free momentum subspaces, whereas fully random noise destroys coherence in a few time-steps. When considering topological edge states, we observe decoherence no matter the type of temporal noise. To explain these results, we derive a non-perturbative master equation to describe the system's dynamics and experimentally confirm our findings in a discrete mesh photonic lattice implemented in a double-fibre ring setup. Surprisingly, our results show that a class of bulk states can be more robust to a certain type of noise than topological edge states.

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 manuscript studies the noisy dynamics of discrete-step quantum walks in a one-dimensional photonic lattice. It reports that temporal noise constant within each Floquet period produces decoherence-free momentum subspaces in the bulk, while fully random temporal noise destroys coherence rapidly; topological edge states decohere under both noise types. A non-perturbative master equation is derived to account for the dynamics, and the results are confirmed experimentally in a double-fibre ring photonic lattice. The central claim is that a class of bulk states can exhibit greater robustness to this specific noise than topological edge states.

Significance. If substantiated, the finding that bulk states can outperform topological edge states under temporally correlated noise offers a new perspective on noise resilience in Floquet-driven systems, potentially useful for photonic quantum information processing. The non-perturbative master equation and the experimental implementation in a fibre-ring setup are strengths that support the practical relevance of the work.

major comments (2)
  1. The derivation of decoherence-free momentum subspaces and the comparative robustness claim rest on the assumption that temporal noise remains constant within each Floquet period (as stated in the abstract and the noise-model section). This intra-period constancy is load-bearing: if the actual noise process has shorter correlation times, the subspaces disappear and the bulk-versus-edge robustness advantage does not hold. The manuscript should provide either an analytic extension or numerical checks showing the sensitivity of the result to violations of this assumption.
  2. Experimental confirmation section: the double-fibre ring implementation must demonstrate that the applied temporal noise satisfies the constant-within-period condition used in the theory. Without explicit verification of the noise correlation time relative to the discrete step or Floquet period, it is unclear whether the experiment actually probes the regime in which the decoherence-free subspaces are predicted to exist.
minor comments (2)
  1. Figure captions should explicitly label the different noise realizations (constant-within-period versus fully random) and the state types (bulk momentum versus edge) to improve readability.
  2. Notation for the master-equation parameters should be cross-checked against the experimental control parameters for consistency.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript arXiv:2510.16204. We address the major comments point by point below and propose revisions to strengthen the presentation of our results on decoherence-free subspaces in noisy quantum walks.

read point-by-point responses

  1. Referee: The derivation of decoherence-free momentum subspaces and the comparative robustness claim rest on the assumption that temporal noise remains constant within each Floquet period (as stated in the abstract and the noise-model section). This intra-period constancy is load-bearing: if the actual noise process has shorter correlation times, the subspaces disappear and the bulk-versus-edge robustness advantage does not hold. The manuscript should provide either an analytic extension or numerical checks showing the sensitivity of the result to violations of this assumption.

    Authors: We agree with the referee that the assumption of temporal noise being constant within each Floquet period is central to the emergence of decoherence-free momentum subspaces. While our non-perturbative master equation is derived under this model, we acknowledge that shorter correlation times would alter the dynamics. In the revised version, we will add numerical checks by simulating noise with varying correlation times shorter than the Floquet period to illustrate the sensitivity and the regime where the subspaces persist. This will provide a clearer picture of the robustness of our findings. revision: yes

  2. Referee: Experimental confirmation section: the double-fibre ring implementation must demonstrate that the applied temporal noise satisfies the constant-within-period condition used in the theory. Without explicit verification of the noise correlation time relative to the discrete step or Floquet period, it is unclear whether the experiment actually probes the regime in which the decoherence-free subspaces are predicted to exist.

    Authors: We thank the referee for highlighting this important aspect of the experimental validation. In our double-fibre ring setup, the temporal noise is implemented by modulating the phase or amplitude in a controlled manner synchronized with the discrete steps. To address this, we will include in the revised manuscript explicit details on the noise generation process, including the measured or designed correlation time, which is engineered to be constant over the Floquet period (spanning multiple steps in the lattice). This verification ensures that the experiment operates in the predicted regime. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation follows from explicit noise model and master equation without self-referential reduction

full rationale

The paper states that decoherence-free momentum subspaces appear in the bulk specifically when temporal noise is constant within each Floquet period, then derives a non-perturbative master equation to describe the dynamics under this condition and contrasts it with fully random noise. This modeling choice is presented as an input assumption rather than a fitted parameter or self-definition; the comparative robustness claim for bulk states versus topological edge states is obtained by applying the same derived equation to both cases. No load-bearing step reduces by construction to a prior self-citation, ansatz smuggled via citation, or renaming of a known result. The experimental implementation in the double-fibre ring setup supplies an independent check outside the analytic derivation, keeping the chain self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the modeling choice that noise is temporally constant within each Floquet period and on the validity of the non-perturbative master equation for the driven lattice.

axioms (1)
  • domain assumption Temporal noise is constant within each Floquet period for the decoherence-free subspace case.
    This condition is explicitly required in the abstract for the bulk decoherence-free subspaces to appear.

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Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    Aharonov, L

    Y. Aharonov, L. Davidovich, and N. Zagury, Quantum random walks, Phys. Rev. A48, 1687 (1993)

    work page 1993

  2. [2]

    M¨ ulken and A

    O. M¨ ulken and A. Blumen, Continuous-time quantum walks: Models for coherent transport on complex net- works, Physics Reports502, 37 (2011)

    work page 2011

  3. [3]

    Schreiber, K

    A. Schreiber, K. N. Cassemiro, V. Potoˇ cek, A. G´ abris, I. Jex, and C. Silberhorn, Decoherence and disorder in quantum walks: From ballistic spread to localization, Phys. Rev. Lett.106, 180403 (2011)

    work page 2011

  4. [4]

    Ambainis, Quantum walks and their algorithmic ap- plications, International Journal of Quantum Informa- tion01, 507 (2003)

    A. Ambainis, Quantum walks and their algorithmic ap- plications, International Journal of Quantum Informa- tion01, 507 (2003)

    work page 2003

  5. [5]

    Shenvi, J

    N. Shenvi, J. Kempe, and K. B. Whaley, Quantum random-walk search algorithm, Phys. Rev. A67, 052307 (2003)

    work page 2003

  6. [6]

    A. M. Childs, Universal Computation by Quantum Walk, Phys. Rev. Lett.102, 180501 (2009)

    work page 2009

  7. [7]

    N. V. Prokof’ev and P. C. E. Stamp, Decoherence and quantum walks: Anomalous diffusion and ballistic tails, Phys. Rev. A74, 020102 (2006)

    work page 2006

  8. [8]

    A. P. Hines and P. C. E. Stamp, Quantum walks, quan- tum gates, and quantum computers, Phys. Rev. A75, 062321 (2007)

    work page 2007

  9. [9]

    Schreiber, A

    A. Schreiber, A. G´ abris, P. P. Rohde, K. Laiho, M. ˇStefaˇ n´ ak, V. Potoˇ cek, C. Hamilton, I. Jex, and C. Sil- berhorn, A 2d quantum walk simulation of two-particle dynamics, Science336, 55 (2012)

    work page 2012

  10. [10]

    C.-W. Lee, P. Kurzy´ nski, and H. Nha, Quantum walk as a simulator of nonlinear dynamics: Nonlinear dirac equation and solitons, Phys. Rev. A92, 052336 (2015)

    work page 2015

  11. [11]

    Vakulchyk, M

    I. Vakulchyk, M. V. Fistul, and S. Flach, Wave Packet Spreading with Disordered Nonlinear Discrete-Time Quantum Walks, Phys. Rev. Lett.122, 040501 (2019)

    work page 2019

  12. [12]

    P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys.79, 135 (2007)

    work page 2007

  13. [13]

    Nahum, S

    A. Nahum, S. Vijay, and J. Haah, Operator Spreading in Random Unitary Circuits, Phys. Rev. X8, 021014 (2018)

    work page 2018

  14. [14]

    Monika, F

    M. Monika, F. Nosrati, A. George, S. Sciara, R. Fazili, A. L. Marques Muniz, A. Bisianov, R. Lo Franco, W. J. Munro, M. Chemnitz, U. Peschel, and R. Morandotti, Quantum state processing through controllable synthetic temporal photonic lattices, Nat. Photon.19, 95 (2025)

    work page 2025

  15. [15]

    Schreiber, K

    A. Schreiber, K. N. Cassemiro, V. Potoˇ cek, A. G´ abris, P. J. Mosley, E. Andersson, I. Jex, and C. Silberhorn, Photons Walking the Line: A Quantum Walk with Ad- justable Coin Operations, Phys. Rev. Lett.104, 050502 (2010)

    work page 2010

  16. [16]

    Wimmer, M.-A

    M. Wimmer, M.-A. Miri, D. Christodoulides, and U. Peschel, Observation of Bloch oscillations in com- plex PT-symmetric photonic lattices, Scientific Reports 6 5, 17760 (2015)

    work page 2015

  17. [17]

    Kitagawa, M

    T. Kitagawa, M. A. Broome, A. Fedrizzi, M. S. Rud- ner, E. Berg, I. Kassal, A. Aspuru-Guzik, E. Demler, and A. G. White, Observation of topologically protected bound states in photonic quantum walks, Nat Commun 3, 882 (2012)

    work page 2012

  18. [18]

    Bisianov, M

    A. Bisianov, M. Wimmer, U. Peschel, and O. A. Egorov, Stability of topologically protected edge states in nonlin- ear fiber loops, Phys. Rev. A100, 063830 (2019)

    work page 2019

  19. [19]

    Weidemann, M

    S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, and A. Szameit, Topological funneling of light, Science368, 311 (2020)

    work page 2020

  20. [20]

    Cardano, A

    F. Cardano, A. D’Errico, A. Dauphin, M. Maffei, B. Pic- cirillo, C. de Lisio, G. De Filippis, V. Cataudella, E. San- tamato, L. Marrucci, M. Lewenstein, and P. Massignan, Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons, Nature Commu- nications8, 15516 (2017)

    work page 2017

  21. [21]

    L. J. Maczewsky, J. M. Zeuner, S. Nolte, and A. Szameit, Observation of photonic anomalous Floquet topological insulators, Nat. Commun.8, 13756 (2017)

    work page 2017

  22. [22]

    Mukherjee, A

    S. Mukherjee, A. Spracklen, M. Valiente, E. Andersson, P. ¨Ohberg, N. Goldman, and R. R. Thomson, Experimen- tal observation of anomalous topological edge modes in a slowly driven photonic lattice, Nature Communications 8, 13918 (2017)

    work page 2017

  23. [23]

    Cheng, Y

    Q. Cheng, Y. Pan, H. Wang, C. Zhang, D. Yu, A. Gover, H. Zhang, T. Li, L. Zhou, and S. Zhu, Observation of AnomalousπModes in Photonic Floquet Engineering, Phys. Rev. Lett.122, 173901 (2019)

    work page 2019

  24. [24]

    A. F. Adiyatullin, L. K. Upreti, C. Lechevalier, C. Evain, F. Copie, P. Suret, S. Randoux, P. Delplace, and A. Amo, Topological Properties of Floquet Winding Bands in a Photonic Lattice, Phys. Rev. Lett.130, 056901 (2022)

    work page 2022

  25. [25]

    Bessho, K

    T. Bessho, K. Mochizuki, H. Obuse, and M. Sato, Ex- trinsic topology of Floquet anomalous boundary states in quantum walks, Phys. Rev. B105, 094306 (2022)

    work page 2022

  26. [26]

    El Sokhen, A

    R. El Sokhen, A. G´ omez-Le´ on, A. F. Adiyatullin, S. Ran- doux, P. Delplace, and A. Amo, Edge-dependent anoma- lous topology in synthetic photonic lattices subject to discrete step walks, Phys. Rev. Res.6, 023282 (2024)

    work page 2024

  27. [27]

    Asapanna, R

    R. Asapanna, R. El Sokhen, A. F. Adiyatullin, C. Hain- aut, P. Delplace, A. G´ omez-Le´ on, and A. Amo, Obser- vation of extrinsic topological phases in floquet photonic lattices, Phys. Rev. Lett.134, 256603 (2025)

    work page 2025

  28. [28]

    Shapira, O

    D. Shapira, O. Biham, A. J. Bracken, and M. Hackett, One-dimensional quantum walk with unitary noise, Phys. Rev. A68, 062315 (2003)

    work page 2003

  29. [29]

    C. M. Chandrashekar, R. Srikanth, and S. Banerjee, Sym- metries and noise in quantum walk, Phys. Rev. A76, 022316 (2007)

    work page 2007

  30. [30]

    Y. Yin, D. E. Katsanos, and S. N. Evangelou, Quantum walks on a random environment, Phys. Rev. A77, 022302 (2008)

    work page 2008

  31. [31]

    Rieder, L

    M.-T. Rieder, L. M. Sieberer, M. H. Fischer, and I. C. Fulga, Localization Counteracts Decoherence in Noisy Floquet Topological Chains, Phys. Rev. Lett.120, 216801 (2018)

    work page 2018

  32. [32]

    L. M. Sieberer, M.-T. Rieder, M. H. Fischer, and I. C. Fulga, Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topo- logical chains, Phys. Rev. B98, 214301 (2018)

    work page 2018

  33. [33]

    Regensburger, C

    A. Regensburger, C. Bersch, B. Hinrichs, G. On- ishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, Photon Propagation in a Discrete Fiber Network: An In- terplay of Coherence and Losses, Phys. Rev. Lett.107, 233902 (2011)

    work page 2011

  34. [34]

    See Supplemental Material accompanying this paper

    work page

  35. [35]

    The data sets correspoding to the figures of this article are available at doi:10.57745/7midra. 7 Master equation for the bulk and stroboscopic noise The time evolution of a state following a time-periodic protocol can be expressed in terms of the Floquet opera- tor as∣ψM⟩= ˆU M F ∣ψ0⟩, whereMis the number of Floquet periods. However, in the presence of n...

    work page doi:10.57745/7midra

  36. [36]

    + 1 2 (1+e −2σ2 ) ( ˆUc ˆρM ˆU † c + ˆU0 ˆρM ˆU † cc + ˆUcc ˆρM ˆU † 0) + 1 2 (1−e −2σ2 ) ( ˆUs ˆρM ˆU † s + ˆU0 ˆρM ˆU † ss + ˆUss ˆρM ˆU †

    work page

  37. [37]

    In this situation the system corresponds to the flat band case and has a fully localized edge state∣e L⟩=(1,0,0,

    + 1 4 (3e−1 2 σ2 +e−9 2 σ2 ) ( ˆUc ˆρM ˆU † cc + ˆUcc ˆρM ˆU † c) + 1 4 (e−1 2 σ2 −e−9 2 σ2 ) ( ˆUc ˆρM ˆU † ss + ˆUss ˆρM ˆU † c + ˆUs ˆρM ˆU † sc + ˆUsc ˆρM ˆU † s) + 1 8 (1−e −8σ2 ) ( ˆUsc ˆρM ˆU † sc + ˆUss ˆρM ˆU † cc + ˆUcc ˆρM ˆU † ss) + 1 8 (3+4e −2σ2 +e−8σ2 ) ˆUcc ˆρM ˆU † cc + 1 8 (3−4e −2σ2 +e−8σ2 ) ˆUss ˆρM ˆU † ss (28) Edge state dynamics und...

    work page