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arxiv: 2604.25311 · v1 · submitted 2026-04-28 · 🪐 quant-ph

Entanglement Dynamics in a Two Transmon Qubit System under Continuous Measurement and Postselection

Roson Nongthombam , Amarendra K. Sarma This is my paper

Pith reviewed 2026-05-07 16:52 UTC · model grok-4.3

classification 🪐 quant-ph
keywords entanglement dynamicscontinuous measurementpostselectiontransmon qubitsPT symmetryexceptional pointstochastic master equationdispersive regime
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The pith

Postselection after continuous measurement slows the decay of entanglement in a two-transmon system compared to unmonitored evolution.

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

The paper studies a pair of transmons coupled dispersively through a shared cavity, where each transmon also emits spontaneously into monitored channels. It derives a postselected master equation from the stochastic evolution and shows that conditioning on measurement records preserves entanglement for longer times than the average, unmonitored dynamics. The Liouvillian spectrum in the interaction frame reveals an exceptional point separating PT-symmetric phases that govern how entanglement decays. A reader would care because entanglement is a resource for quantum information, and postselection offers a passive route to protect it against dissipation without active feedback.

Core claim

In the dispersive regime the two transmons interact via virtual cavity photons while their spontaneous emissions are continuously monitored; postselection on the detection records yields a non-Hermitian effective dynamics whose entanglement lifetime is substantially longer than that of the corresponding unmonitored master equation, with the transition between unbroken and broken PT-symmetric phases marked by an exceptional point in the Liouvillian spectrum.

What carries the argument

The postselected master equation obtained by conditioning the stochastic master equation on efficient or inefficient detector records, whose spectrum exhibits an exceptional point separating PT-symmetric phases.

If this is right

  • Postselection extends the usable lifetime of entanglement even when detectors are inefficient.
  • The PT-symmetric phases identified in the Liouvillian control the qualitative shape of the entanglement decay curves.
  • The same conditioning procedure can be applied to other monitored dissipative systems to engineer longer-lived entangled states.
  • The exceptional point provides a tunable parameter for switching between different dynamical regimes of entanglement.

Where Pith is reading between the lines

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

  • Similar postselection protocols might be tested in other circuit-QED architectures to protect entanglement against photon loss.
  • The approach could be combined with active feedback to further extend coherence times in near-term superconducting processors.
  • The observed slowing may connect to measurement-induced phase transitions studied in many-body monitored systems.

Load-bearing premise

The system remains deep in the dispersive regime so that the effective transmon-transmon coupling via virtual cavity excitation holds and detector inefficiencies do not erase the qualitative slowing of entanglement decay.

What would settle it

An experiment that measures the entanglement decay rate for the same two-transmon circuit both with and without postselection on the emission records and finds no difference would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.25311 by Amarendra K. Sarma, Roson Nongthombam.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of a transmon–cavity–transmon cou view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy (eigenvalue) spectrum of (a) a single transmon view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the real and imaginary parts of the density matrix elements for (a,d) the transmon-cavity-transmon view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison between the trajectory ensemble average (dotted curve) and the average dynamics obtained from the master view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Comparison of the two-transmon entanglement view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Eigenvalue spectrum of the Liouvillian superoperator (a-d) and the corresponding evolution of density matrix elements view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Eigenvalue spectrum of the Liouvillian superoperator view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Real (a,c) and imaginary (b,d) parts of the density view at source ↗
read the original abstract

We investigate the role of continuous measurement and postselection in the dynamics and entanglement of a transmon-cavity-transmon coupled system. In the dispersive regime, characterized by a large detuning between the transmons and the cavity, the two transmons interact via virtual excitation of the cavity, giving rise to an effective transmon-transmon coupling. In addition to this coherent interaction, each transmon undergoes spontaneous emission, which is continuously monitored through independent detection channels. By incorporating realistic detector inefficiencies, we analyze both efficient and imperfect monitoring scenarios and demonstrate that postselection significantly slows down the decay of entanglement compared to the unmonitored case. We formulate the stochastic master equation for the coupled system, derive the corresponding postselected master equation, and investigate the dynamics through the Liouvillian superoperator spectrum. In the interaction frame, we identify the emergence of an exceptional point and characterize the associated broken and unbroken PT-symmetric phases. We show how these phases influence the system dynamics and the corresponding entanglement behavior. Our results provide insight into how continuous measurement and postselection affect entanglement in dissipative quantum systems, with potential applications in quantum information processing.

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 entanglement dynamics in a two-transmon system coupled via a cavity in the dispersive regime. It derives the stochastic master equation incorporating continuous monitoring of spontaneous emission (with realistic detector inefficiencies), obtains the corresponding postselected master equation, and analyzes the Liouvillian spectrum to identify an exceptional point separating broken and unbroken PT-symmetric phases. The central claim is that postselection significantly slows the decay of entanglement relative to the unmonitored case.

Significance. If the central claim holds, the work provides concrete insight into how postselection can protect entanglement in dissipative qubit systems, with potential relevance to quantum information tasks. The derivation of both stochastic and postselected master equations followed by Liouvillian spectral analysis (including PT-phase characterization) constitutes a systematic and reproducible approach; the explicit inclusion of detector inefficiencies is a realistic strength.

major comments (1)
  1. [Abstract and effective Hamiltonian derivation] Abstract and the section deriving the effective transmon-transmon coupling: the large-detuning dispersive approximation is used to eliminate the cavity degree of freedom and obtain the effective interaction. Continuous monitoring of spontaneous emission, however, introduces measurement backaction that can populate the cavity mode, potentially violating the large-detuning assumption. No explicit verification (e.g., comparison of full versus effective Hamiltonian trajectories or variation of detuning/inefficiency parameters) is provided to confirm that the reported slowing of entanglement decay survives this backaction. This assumption is load-bearing for both the postselected master equation and the subsequent Liouvillian/PT-phase analysis.
minor comments (2)
  1. [Derivation of postselected master equation] Clarify the precise definition of the postselection probability and its normalization in the postselected master equation; the transition from the stochastic to the postselected equation should be written with explicit averaging over the monitored trajectories.
  2. [Liouvillian analysis] In the Liouvillian spectrum plots or tables, label the exceptional point explicitly and indicate the parameter values at which the PT phases transition.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for their positive assessment of the work's significance. We address the major comment below and will incorporate additional verification in the revised version.

read point-by-point responses

  1. Referee: Abstract and the section deriving the effective transmon-transmon coupling: the large-detuning dispersive approximation is used to eliminate the cavity degree of freedom and obtain the effective interaction. Continuous monitoring of spontaneous emission, however, introduces measurement backaction that can populate the cavity mode, potentially violating the large-detuning assumption. No explicit verification (e.g., comparison of full versus effective Hamiltonian trajectories or variation of detuning/inefficiency parameters) is provided to confirm that the reported slowing of entanglement decay survives this backaction. This assumption is load-bearing for both the postselected master equation and the subsequent Liouvillian/PT-phase analysis.

    Authors: We agree that the validity of the dispersive approximation under continuous monitoring requires explicit verification, as the measurement backaction could in principle affect cavity population. In our model, spontaneous emission is treated as independent decay channels from each transmon to its own environment, with monitoring applied to the corresponding jump operators (which act on the transmon subspace). The effective Hamiltonian is obtained via standard Schrieffer-Wolff transformation in the large-detuning limit (Δ ≫ g, κ), where the cavity remains virtually populated. The stochastic terms in the master equation incorporate the backaction on the transmons without directly driving the cavity mode in the effective description. Nevertheless, to address the referee's concern rigorously, the revised manuscript will include an appendix with direct numerical comparisons: (i) stochastic trajectories of the full transmon-cavity-transmon Hamiltonian versus the effective two-qubit model, and (ii) scans over detuning and detector inefficiency. These will confirm that cavity population remains negligible and that the reported slowing of entanglement decay, as well as the Liouvillian spectrum and PT-phase structure, are preserved for the parameter regime used in the main text. revision: yes

Circularity Check

0 steps flagged

Derivation chain follows standard quantum optics procedures without reduction to inputs

full rationale

The paper formulates the stochastic master equation from continuous monitoring of spontaneous emission and derives the postselected master equation directly from it, both of which are standard operations in quantum trajectory theory. The Liouvillian spectrum is then computed from the postselected equation to extract exceptional points and PT phases, again a direct linear-algebra step with no parameter fitting or redefinition involved. The dispersive-regime effective coupling is introduced as an input approximation under large detuning, not derived circularly from the target entanglement dynamics. No self-citations, ansatzes smuggled via prior work, or fitted inputs renamed as predictions appear in the chain. The overall derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claims rest on the standard open-quantum-system formalism and the dispersive approximation; no new free parameters, ad-hoc entities, or non-standard axioms are introduced in the abstract.

axioms (2)
  • domain assumption Dispersive regime with large detuning between transmons and cavity
    Invoked to obtain effective transmon-transmon coupling via virtual excitation.
  • standard math Validity of the stochastic master equation for continuous monitoring
    Used as the starting point for deriving the postselected dynamics.

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