CoChat
Sign Up
Cited by 3Quantum Mechanics and Non-Hermitian PhysicsQuantum Mechanics and ApplicationsQuantum optics and atomic interactions

The DOI matches its Crossref record; 90 of the 90 references it cites were found in a registry or an index; 5 of the 7 sources its claims cite were checked for support.

Non-Hermitian interacting quantum walks of correlated photons

Open access
Wan, Tuo, Yang, Zhaoju·2025·Communications Physics
DOI 10.1038/s42005-025-02038-9
Open this paper in CoChat — free account

Abstract

The non-Hermitian skin effect (NHSE), referring to the anomalous localization of eigenstates, has been widely discussed in single-particle systems. However, the interplay between the interacting NHSE and the quantum optical phenomena remains elusive. Here, We present the non-Hermitian quantum walks of strongly correlated photon pairs. Through studying the dynamic behavior of the photon pairs in the nonreciprocal Bose-Hubbard chain, we theoretically demonstrate the interplay between interactions and the NHSE. When launching two non-entangled photons, the photons exhibit the nonreciprocal bunching effect, which can be suppressed by the interactions. When launching two path-entangled photons, the interactions can not only suppress but reverse the nonreciprocal bunching. In stark contrast to the common wisdom that the NHSE suppresses the entanglement of the quantum many-body system, the entanglement of the photons here can be significantly enhanced. Our results reveal that many-body interactions and entanglement significantly restrain the non-Hermitian nonreciprocal quantum dynamics, offering insights into the interplay between many-body quantum entanglement and non-Hermitian physics. The non-Hermitian skin effect, which nonreciprocally accumulates particles at the boundary, generally suppresses entanglement by constraining global correlations. Here, the authors demonstrate that interactions can suppress nonreciprocal bunching, while entangled photons can reverse bunching direction, leading to enhanced entanglement.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper theoretically studies non-Hermitian interacting quantum walks of correlated photon pairs in a nonreciprocal Bose-Hubbard chain, revealing interplay between interactions, entanglement, and the non-Hermitian skin effect (NHSE). It finds that nonreciprocal bunching can be suppressed or reversed and that entanglement entropy can be enhanced, contrary to the usual expectation that NHSE suppresses entanglement.

Key findings

  • In the nonreciprocal chain, the NHSE drives two photons toward the right edge, producing a nonreciprocal bunching effect; many-body interactions suppress this bunching, and strong interactions lead to antibunching competing with the NHSE.
  • For path-entangled NOON input states, with fixed phase θ = π/2 and moderate interaction strength U = 2, the nonreciprocal bunching reverses from right- to left-bunching, indicated by a negative bunching imbalance \({{{\mathcal{I}}}}\); this reversal does not occur in the Hermitian case.
  • Disorder competes with the nonreciprocal bunching effect and pushes the crossover boundary of \({{{\mathcal{I}}}}=0\) to stronger interaction regions.
  • The half-chain entanglement entropy can be significantly enhanced in the non-Hermitian case, as shown by a positive peninsula in \(\Delta S = S_{\mathrm{NH}} - S_{\mathrm{H}}\), contrary to the common wisdom that NHSE suppresses entanglement.

Methods

  • Theoretical model: a two-particle Bose-Hubbard chain with nonreciprocal couplings \(t_1, t_2\) and on-site interaction \(U\), mapped to a two-dimensional synthetic lattice; analyzed via periodic/open boundary spectra, correlation matrices, and quantum walk dynamics.
  • Initial states: two adjacent non-entangled photons \(| \psi_{\mathrm{initial}} \rangle = c_1^\dagger c_0^\dagger |0\rangle\), and path-entangled NOON states \(| \psi_{\mathrm{initial}} \rangle = \frac{1}{2}(c_0^{\dagger 2} + e^{i\theta} c_1^{\dagger 2})\). Observables include bunching imbalance \({{{\mathcal{I}}}}\) and half-chain entanglement entropy \(S = -\mathrm{Tr}[\rho_A \log_2(\rho_A)]\).
  • Disorder is introduced as \(H_w = H + \sum_n W_n c_n^\dagger c_n\), with \(W_n \in [-w/2, w/2]\); disorder strength is swept. An experimental proposal for ultracold atoms and superconducting circuits is given in Supplementary Note 3.

Limitations

  • The paper does not include a dedicated limitations section and does not explicitly state limitations.
  • Evident from the text: the work is theoretical, with experimental accessibility discussed only in Supplementary Note 3; no experimental realization or experimental data are presented in the main text.
  • Evident from the text: data for all main-text figures are provided in Supplementary Data 1, while other data and codes are available only upon reasonable request to the corresponding author.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/s42005-025-02038-9

Cites

90 of 90 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

5 of 7 cited sources checked · 2 supported · 0 flagged · accuracy not yet measured

  • Premisecitation
    § Introduction

    Under appropriate approximation, a dissipative open quantum system can be mapped to a non-Hermitian Hamiltonian.

    “Under appropriate approximation, the dissipative open quantum system can be mapped to a non-Hermitian Hamiltonian2.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [2] Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-hermitian systems. Rev. Mod. Phys. 93, 015005 (2021). source
  • Findingown data
    § Abstract

    For two path-entangled photons, interactions can reverse the nonreciprocal bunching.

    “When launching two path-entangled photons, the interactions can not only suppress but reverse the nonreciprocal bunching.”
    • Also stated in: § Results · plain
      “with adequate values of the phase θ, the nonreciprocal bunching effect can be reversed.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Results

    In the case of strong interaction strength, the Fermionization process prevails, resulting in an antibunching correlation in the Hermitian scenario.

    “In the case of strong interaction strength, the Fermionization process prevails, resulting in an antibunching correlation in the Hermitian scenario, as depicted in Fig. 2g.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Results

    For doublon skin states, enhanced diagonal elements in the correlation map indicate two particles occupy the same site, forming doublon states.

    “Two features emerge for the doublon skin states’ correlation map: (i) Enhanced diagonal elements indicate two particles occupy the same site, forming doublon states.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Results

    The entropy pattern is symmetric with respect to θ = π in the Hermitian case.

    “The pattern is symmetric with respect to the axis of θ = π in the Hermitian case [panel (b)].”
    Quote in the paperNot a substantial claim
  • It may state two separate claims as one. 11
  • Probably not a substantial claim. 1

  • It may state two separate claims as one.

    Interpretationcitation
    § Results

    The dimensional transposition of the one-dimensional two-particle chain yields a synthetic lattice with nonreciprocal couplings in both the x and y directions, indicating high-order skin corner modes.

    “As a result of this dimensional transposition, we observe the formation of a synthetic lattice that exhibits nonreciprocal couplings in both the x and y directions, indicating the existence of the high-order skin corner modes88,89,90,91.”
    Quote in the paperSubstantial claim4 of 4 sources checked
    • cites [88] Kawabata, K., Sato, M. & Shiozaki, K. Higher-order non-hermitian skin effect. Phys. Rev. B 102, 205118 (2020). source

      The Introduction and Conclusion describe a two-dimensional higher-order non-Hermitian skin effect with corner-localized skin modes. The cited paper does not describe dimensional transposition of a one-dimensional two-particle chain into the synthetic lattice claimed here, so it supports the corner-mode concept but not that specific construction. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
    • cites [89] Okugawa, R., Takahashi, R. & Yokomizo, K. Second-order topological non-hermitian skin effects. Phys. Rev. B 102, 241202 (2020). source
    • cites [90] Fu, Y., Hu, J. & Wan, S. Non-hermitian second-order skin and topological modes. Phys. Rev. B 103, 045420 (2021). source

      Section II.B describes second-order skin corner modes arising from skin effects along both lattice directions, supporting the proposed link between two-directional skin effects and corner localization. But Section III.A starts with a two-dimensional tight-binding model; our copy does not describe obtaining a synthetic lattice by dimensionally transposing a one-dimensional two-particle chain. (LLM, conf=0.85)

      Experimental — accuracy not yet measured
    • cites [91] Zhang, X., Tian, Y., Jiang, J.-H., Lu, M.-H. & Chen, Y.-F. Observation of higher-order non-hermitian skin effect. Nat. Commun. 12, 5377 (2021). source

      The Results section (‘Spinful HOTIs and the higher-order non-Hermitian skin effect’; page unavailable) describes direction-dependent couplings in a two-dimensional sonic crystal and corner-localized skin modes when both x and y boundaries are opened. It does not describe dimensional transposition of a one-dimensional two-particle chain or a synthetic lattice produced by that transposition. (LLM, conf=0.86)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Findingown data
    § Results

    For repulsive skin states, the correlation matrix shows non-diagonal dominance, though these modes also exhibit the skin effect and localize towards the upper right corner.

    “In contrast, the correlation matrix for repulsive skin states shows non-diagonal dominance, though these modes also exhibit the skin effect and localize towards the upper right corner.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data
    § Results

    For doublon skin states, correlation is concentrated in the upper right corner and decays towards the bulk, indicating localization at the right edge and demonstrating the NHSE.

    “(ii) Correlation concentrated in the upper right corner and decaying towards the bulk suggests the localization at the right edge, demonstrating the feature of the NHSE.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingnone given
    § Introduction

    In the presence of nonreciprocal couplings, the energy spectrum of the quantum walk is complex and the eigenstates exhibit the non-Hermitian skin effect.

    “In the presence of nonreciprocal couplings, the energy spectrum of the quantum walk is now complex and the eigenstates exhibit the NHSE.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingown data
    § Results

    The crossover boundary of the bunching effect is pushed to the strong interaction region with increasing disorder strength, providing an additional degree of freedom to control the direction of the nonreciprocal bunching.

    “Consequently, the crossover boundary of the bunching effect is pushed to the strong interaction region with increasing disorder strength, which provides an additional degree of freedom to control the direction of the nonreciprocal bunching.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Disorder can lead to Anderson localization, which competes with the nonreciprocal bunching effect and causes the bunching imbalance to vanish.

  • It may state two separate claims as one.

    Findingreasoning
    § Results

    Increasing interaction strength U diminishes the right-bunching states and reverses the bunching direction for entangled photons.

    “As shown in Fig. 3b–d, increasing the interaction strength U diminishes the right-bunching states and reverses the bunching direction.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingcitation
    § Results

    With increasing interaction strength, the Fermionization process competes with reciprocal and nonreciprocal bunching, while non-bunching states become more prevalent.

    “With increasing interaction strength, the Fermionization process85 starts competing with the reciprocal bunching [Fig. 2c] and the nonreciprocal bunching effect [Fig. 2d], while non-bunching states progressively become more prevalent [Fig. 2e, f].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [85] Lahini, Y. et al. Quantum walk of two interacting bosons. Phys. Rev. A 86, 011603 (2012). source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Findingreasoning
    § Introduction

    With nonreciprocal couplings, the reciprocal bunching of indistinguishable photons at two sides is disintegrated and the photons bunch toward the right side of the chain, corresponding to the direction of the non-Hermitian skin effect.

    “Consequently, the reciprocal bunching of the indistinguishable photons at two sides of the quantum walk is disintegrated and the photons are bunching towards one side of the chain, which is the key signature of the non-Hermitian skin effect.”
    • Also stated in: § Results · plain
      “As depicted in Fig. 2b, the reciprocal bunching of the indistinguishable photons at two sides is disintegrated, and the photons bunch toward the right side of the chain, which corresponds to the direction of the NHSE.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given
    § Conclusions

    The proposed model should be easily accessible in current cutting-edge quantum simulators based on ultracold atoms and superconducting circuits.

    “The proposed model should be easily accessible in the current cutting-edge quantum simulators based on ultracold atoms and superconducting circuits (see Supplementary Note 3 for the experimental proposal).”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning
    § Results

    The reversed nonreciprocal bunching effect can be explained by interference: when launching the path-entangled input state, two photons occupy the same site, exciting only doublon skin modes.

    “This reversed nonreciprocal bunching effect can be explained by the interference: when launching the path-entangled input state, two photons occupy the same site, exciting only doublon skin modes.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationreasoning
    § Results

    This interaction-dependent phenomenon competes significantly with the NHSE in the non-Hermitian case, inducing the transition of the nonreciprocal bunching effect.

    “This interaction-dependent phenomenon competes significantly with the NHSE in the non-Hermitian case, thus inducing the transition of the nonreciprocal bunching effect.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationown data
    § Conclusions

    The non-Hermitian interacting quantum walk of correlated photons reveals unique dynamical features, such as reversed nonreciprocal dynamics and entanglement enhancement, which differ from the typical NHSE.

    “In conclusion, we have investigated the non-Hermitian interacting quantum walks of correlated photons, revealing unique dynamical features, such as reversed nonreciprocal dynamics and entanglement enhancement, which differ from the typical NHSE.”
    Quote in the paperSubstantial claim
12 of 12

  • The paper relies on this without support.

    The study of the interplay between the interacting NHSE and quantum optical phenomena such as photon interference and entanglement remains elusive.

    “However, up to now, the study of the interplay between the interacting NHSE and the quantum optical phenomena such as photon interference and entanglement remains elusive.”

  • The paper relies on this without support.

    Disorder can lead to Anderson localization, which competes with the nonreciprocal bunching effect and causes the bunching imbalance to vanish.

    “Generally speaking, the disorder can lead to the Anderson localization, which competes with the nonreciprocal bunching effect and causes the bunching imbalance to vanish.”
2 of 2

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Kawabata, K., Numasawa, T. & Ryu, S. Entanglement phase transition induced by the non-hermitian skin effect. Phys. Rev. X 13, 021007 (2023).

Cited by

Sorted by citations

Related

Metadata

Authors
Wan, T., & Yang, Z.
Affiliations
Zhejiang University (CN)
Corresponding author
Yang, Zhaoju
ORCID
Yang, Zhaoju
Venue
Communications Physics
Publisher
Springer Science and Business Media LLC
Published
2025-04-01
Volume
8
Issue
1
ISSN
2399-3650 (ISSN-L)
DOI
10.1038/s42005-025-02038-9
OpenAlex
W4409082702
Cited by
3
References
90
Citations by year
2026: 2 · 2025: 1
FWCI
0.88
Type
journal article
Language
en
Open access
Licence
Locations
  • Communications Physics (publishedVersion, cc-by-nc-nd)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
  • National Natural Science Foundation of China (No. 12174339)
  • Natural Science Foundation of Zhejiang Province (No. LR23A040003)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
Keywords
non-Hermitian skin effect, entanglement enhancement, path-entangled photons, many-body interactions

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

A language model drew the claims from the paper on 2026-11-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).

A second model labelled each claim on 2026-11-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).

Cited sources are checked with a language model’s help (gpt-6-sol).

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review