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arxiv: 2507.22796 · v2 · submitted 2025-07-30 · 🪐 quant-ph

Decoherence-free subspaces and Markovian revival of genuine multipartite entanglement in a dissipative system

Shubhodeep Gangopadhyay , Vinayak Jagadish , R. Srikanth This is my paper

Pith reviewed 2026-05-19 02:39 UTC · model grok-4.3

classification 🪐 quant-ph
keywords genuine multipartite entanglementdecoherence-free subspacesMarkovian revivalsuperradiancesubradiancecollective dissipationopen quantum systems
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The pith

Genuine multipartite entanglement revives in the Markovian regime of a collective qubit-bath system through interference with a decoherence-free subspace.

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

The paper studies how n qubits (n at least 3) that share one bosonic bath at zero temperature evolve their genuine multipartite entanglement when restricted to the single-excitation sector. Collective coupling splits the space into a decaying superradiant mode and an orthogonal subradiant subspace that stays invariant under dissipation because of the symmetry of the interaction. For three qubits the authors track the convex-roof negativity and locate parameter windows set by the Lorentzian bath spectrum and coupling strengths. In the Markovian limit they show that genuine tripartite entanglement can return transiently even though the bath has no memory, because the decaying amplitude interferes destructively with the protected component. This matters for open-system quantum information because it demonstrates that symmetry-protected subspaces can produce entanglement revivals without invoking non-Markovian effects.

Core claim

Restricting the dynamics to the single-excitation sector, the collective system-bath coupling separates the Hilbert space into a superradiant mode that decays and a decoherence-free subradiant subspace. In the three-qubit case the convex-roof extension of negativity reveals that, in the Markovian limit, genuine tripartite entanglement exhibits a nontrivial revival arising from destructive interference between the decaying superradiant component and the invariant subradiant subspace under suitable collective coupling strengths and bath parameters.

What carries the argument

the collective system-bath coupling that partitions the single-excitation manifold into a decaying superradiant mode and an invariant decoherence-free subradiant subspace

Load-bearing premise

The analysis is limited to the single-excitation sector and assumes a Lorentzian spectral density that cleanly separates superradiant and subradiant modes.

What would settle it

Track the convex-roof negativity of genuine tripartite entanglement for three collectively coupled qubits tuned to the predicted Markovian parameter regime; the absence of a revival after initial decay would falsify the interference mechanism.

Figures

Figures reproduced from arXiv: 2507.22796 by R. Srikanth, Shubhodeep Gangopadhyay, Vinayak Jagadish.

Figure 1
Figure 1. Figure 1: FIG. 1: (Color Online) The dynamics of tripartite [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

We investigate the dynamics of genuine multipartite entanglement (GME) in a system of $n$ qubits ($n\ge3$) collectively interacting with a common zero temperature bosonic bath characterized by a Lorentzian spectral density. Restricting the dynamics to the single excitation sector, the collective system-bath coupling naturally separates the Hilbert space into a superradiant mode and a subspace of states orthogonal to it, which forms a decoherence free (subradiant) subspace. We show that this symmetry induced structure leads to persistent components of the state that remain protected from dissipation. Specifically, in the three qubit case, the time evolution of genuine tripartite entanglement is analyzed using the convex roof extension of negativity. We identify parameter regimes determined by the bath spectral density and collective coupling strengths that correspond to Markovian and non-Markovian dynamics. In the Markovian limit, we demonstrate that GME can exhibit a nontrivial revival even in the absence of environmental memory effects. This revival arises from the destructive interference between the decaying superradiant component and the invariant subradiant subspace under suitable system configuration, leading to a transient loss of GME.

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 / 2 minor

Summary. The manuscript investigates genuine multipartite entanglement (GME) dynamics for n qubits (n≥3) collectively coupled to a zero-temperature bosonic bath with Lorentzian spectral density. Restricting to the single-excitation sector, collective coupling decomposes the space into a decaying superradiant mode and an invariant subradiant decoherence-free subspace. For three qubits, the convex-roof extension of negativity is employed to track GME; parameter regimes distinguishing Markovian and non-Markovian regimes are identified. The central result is that, in the Markovian limit, GME exhibits a nontrivial revival arising from destructive interference between the decaying superradiant component and the protected subradiant subspace, without environmental memory effects.

Significance. If the central claim holds, the work provides a concrete mechanism for GME revival in purely Markovian open-system dynamics via symmetry-protected subspaces, separating this phenomenon from the non-Markovian memory effects usually invoked for revivals. The clean separation enabled by collective coupling to a Lorentzian bath and the explicit use of convex-roof negativity for the tripartite case constitute a falsifiable prediction with potential experimental relevance in platforms exhibiting collective dissipation.

major comments (1)
  1. [§ on three-qubit GME dynamics] § on three-qubit GME dynamics (Markovian limit paragraph): the demonstration of revival relies on the relative amplitude evolution between superradiant and subradiant components producing non-monotonic convex-roof negativity; however, the explicit time-dependent expressions or numerical parameter values (collective couplings and spectral width) that generate the reported transient loss and revival are not stated, preventing direct verification of the interference mechanism.
minor comments (2)
  1. [Model section] The justification for restricting the analysis to the single-excitation sector and its implications for the n≥3 claim should be expanded with a brief argument why higher-excitation sectors do not qualitatively alter the Markovian revival.
  2. [Notation] Notation for the bath spectral density parameters and collective coupling strengths should be introduced with explicit symbols at first use to aid reproducibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the constructive comment. We address the point raised below and have revised the manuscript accordingly to improve clarity and verifiability.

read point-by-point responses

  1. Referee: [§ on three-qubit GME dynamics] § on three-qubit GME dynamics (Markovian limit paragraph): the demonstration of revival relies on the relative amplitude evolution between superradiant and subradiant components producing non-monotonic convex-roof negativity; however, the explicit time-dependent expressions or numerical parameter values (collective couplings and spectral width) that generate the reported transient loss and revival are not stated, preventing direct verification of the interference mechanism.

    Authors: We appreciate the referee drawing attention to this issue of explicit verifiability. In the single-excitation sector the collective dynamics decouples exactly into a superradiant mode |S⟩ = ( |100⟩ + |010⟩ + |001⟩ )/√3 that decays at rate Γ = 3γ (where γ is the single-qubit decay rate set by the Lorentzian peak) and an orthogonal two-dimensional subradiant subspace that remains invariant. Consequently the time-evolved state takes the closed form |ψ(t)⟩ = a(t) |S⟩ + |ψ_sub⟩ with a(t) = a(0) exp(−Γ t) in the Markovian limit (spectral width λ ≫ Γ). The convex-roof negativity is then a non-monotonic function of |a(t)| because the subradiant component interferes destructively with the decaying amplitude. To make this transparent we have added the explicit expression for N(t) together with the concrete parameter set used for the reported revival: collective coupling strength such that Γ = 1, Markovian regime λ = 10, and initial state |ψ(0)⟩ = (|100⟩ + |010⟩ + |001⟩)/√3. These additions appear in the revised Markovian-limit paragraph and in a new footnote that lists the numerical values employed in the figures. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation proceeds from the collective system-bath interaction Hamiltonian under a Lorentzian spectral density, which by symmetry decomposes the single-excitation subspace into a decaying superradiant mode and an invariant subradiant subspace. The Markovian revival of GME is obtained by direct integration of the resulting master equation and evaluation of the convex-roof negativity; the non-monotonic behavior follows from the relative phase and amplitude evolution between the two components without any fitted parameter being redefined as a prediction or any load-bearing premise resting on a self-citation chain. The analysis remains self-contained within the single-excitation sector and the stated bath assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the single-excitation restriction and the assumption that collective coupling produces cleanly separable superradiant and subradiant subspaces; no new particles or forces are postulated.

free parameters (1)
  • Collective coupling strengths and bath spectral width
    These parameters determine the Markovian versus non-Markovian regimes and the interference condition for revival; their specific values are not derived from first principles.
axioms (2)
  • domain assumption Collective system-bath interaction in the single-excitation sector separates the Hilbert space into superradiant and decoherence-free subradiant subspaces
    Invoked to explain persistent components protected from dissipation.
  • domain assumption Zero-temperature bosonic bath with Lorentzian spectral density
    Chosen to model the environment and enable analytic separation of modes.

pith-pipeline@v0.9.0 · 5744 in / 1369 out tokens · 39989 ms · 2026-05-19T02:39:13.894130+00:00 · methodology

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Reference graph

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