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arxiv: 2606.03293 · v1 · pith:TYQNPPECnew · submitted 2026-06-02 · 🪐 quant-ph

Deterministic generation of cat states with more than 100 photons under dissipation

Zhu-yao Jin , Jun Jing This is my paper

Pith reviewed 2026-06-28 09:52 UTC · model grok-4.3

classification 🪐 quant-ph
keywords cat statesdynamical invarianthybrid qubit-boson systemsnon-Hermitian dynamicsuniversal quantum controlmacroscopic quantum statesdeterministic generationtime-dependent Hamiltonian
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The pith

A balanced qubit superposition drives a bosonic mode deterministically from vacuum to a cat state with over 120 photons.

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

The paper establishes a method to produce large cat states in a hybrid qubit-boson system by engineering time-dependent Hamiltonians that obey constraints set by the system's dynamical invariant. The qubit begins in an equal superposition of its states, after which the bosonic mode evolves from the vacuum into a macroscopic superposition whose mean photon number exceeds 120. This evolution remains deterministic in both the Hermitian case, where it reaches perfect fidelity, and the non-Hermitian case under dissipation, where fidelity stays above 0.962. The approach also extends to intrinsic and four-component cat states while advancing universal quantum control into hybrid discrete-continuous systems.

Core claim

When the qubit is prepared in a balanced superposed state, the bosonic mode can evolve deterministically from the vacuum state to the cat state of a mean photon number over 120. In the Hermitian case, the generation is perfect; and in the non-Hermitian case, the fidelity is over 0.962. The controllable dynamics are encoded in the evolution of the dynamical invariant, which is analyzed in the ancillary picture via a unitary transformation conditional on the qubit state and constrained by the Heisenberg equation.

What carries the argument

Dynamical invariant of the hybrid qubit-bosonic system, whose evolution under the Heisenberg equation imposes constraints on the time-dependent Hamiltonian.

If this is right

  • The same protocol generates intrinsic cat states and four-component cat states of comparably large size.
  • Universal quantum control extends directly to hybrid discrete-continuous variable systems.
  • Macroscopic quantum states remain reachable even when decoherence is modeled by non-Hermitian dynamics.
  • Deterministic evolution holds from the vacuum state whenever the qubit starts in a balanced superposition.

Where Pith is reading between the lines

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

  • If real-time Hamiltonian engineering proves feasible in circuit-QED hardware, the method could produce cat states with several hundred photons.
  • The ancillary-picture approach may generalize to other hybrid platforms such as optomechanical systems for generating macroscopic superpositions.
  • Combining this invariant-based control with error-correction codes could stabilize large cat states against additional noise channels not treated in the paper.
  • The protocol's reliance on a single qubit suggests it could be scaled by entangling multiple qubits to produce multi-mode entangled cat states.

Load-bearing premise

The time-dependent Hamiltonian can be engineered in real time to exactly satisfy the constraints imposed by the Heisenberg equation on the dynamical invariant.

What would settle it

An experiment applying the prescribed time-dependent Hamiltonian to a qubit-boson system but measuring a final-state fidelity below 0.9 to the target cat state under dissipation would falsify the deterministic generation claim.

Figures

Figures reproduced from arXiv: 2606.03293 by Jun Jing, Zhu-yao Jin.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the open hybrid qubit-bosonic system, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Wigner functions of specific moments [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dynamics of the density-matrix trace about the whole [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Dynamics of the density-matrix trace of Tr( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Large-size cat states are especially meaningful and fundamental for exploring the quantum-to-classical transition, as well as promising resources for quantum metrology and fault-tolerant quantum computation. However, amplifying the magnitude of cat states remains challenging because of the growing fragility under decoherence. We propose to generate large cat states by using the dynamical invariant of hybrid qubit-bosonic systems under Hermitian or non-Hermitian time-dependent Hamiltonian. It is a study with the universal quantum control (UQC) theory, in which the system dynamics is analyzed in the ancillary picture via a unitary transformation conditional on the qubit state. The controllable dynamics that can be encoded in the evolution of the dynamical invariant is presented by the Heisenberg equation, which imposes constrains on the Hamiltonian. When the qubit is prepared in a balanced superposed state, the bosonic mode can evolve deterministically from the vacuum state to the cat state of a mean photon number over $120$. In the Hermitian case, the generation is perfect; and in the non-Hermitian case, the fidelity is over $0.962$. Our protocol can also be applied to the generation of the intrinsic cat states and the four-component cat states of large size. Through the preparation of macroscopic quantum states, our work essentially advances UQC to hybrid discrete-continuous variable systems.

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 / 0 minor

Summary. The manuscript proposes generating large cat states (>120 mean photons) deterministically in hybrid qubit-bosonic systems from the vacuum state by using dynamical invariants under time-dependent Hermitian or non-Hermitian Hamiltonians. The dynamics are analyzed in the ancillary picture via a conditional unitary transformation within universal quantum control (UQC) theory; the Heisenberg equation imposes constraints on the Hamiltonian. The qubit is prepared in a balanced superposition, yielding perfect fidelity in the Hermitian case and fidelity >0.962 in the non-Hermitian case. The protocol is also applied to intrinsic and four-component cat states.

Significance. If the central claims are substantiated, the work would advance the deterministic preparation of macroscopic quantum states with over 100 photons, which are relevant for quantum-to-classical transition studies, quantum metrology, and fault-tolerant quantum computation. The extension to non-Hermitian dynamics under dissipation addresses realistic open-system conditions, and the UQC framework applied to hybrid discrete-continuous variable systems offers a potentially generalizable approach.

major comments (1)
  1. [Abstract (UQC analysis paragraph)] Abstract (UQC analysis paragraph): The fidelity result (>0.962) for the non-Hermitian case rests on the ancillary-picture unitary transformation remaining valid throughout the evolution. Non-Hermitian Hamiltonians generate non-unitary dynamics, so the conditional unitary and its compatibility with the Heisenberg-equation constraints on the dynamical invariant require explicit justification rather than following automatically from the Hermitian UQC framework. This is load-bearing for the non-Hermitian claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of the significance of our work and for the constructive comment. We address the major comment below.

read point-by-point responses

  1. Referee: The fidelity result (>0.962) for the non-Hermitian case rests on the ancillary-picture unitary transformation remaining valid throughout the evolution. Non-Hermitian Hamiltonians generate non-unitary dynamics, so the conditional unitary and its compatibility with the Heisenberg-equation constraints on the dynamical invariant require explicit justification rather than following automatically from the Hermitian UQC framework. This is load-bearing for the non-Hermitian claim.

    Authors: We agree that the non-Hermitian extension requires explicit justification rather than automatic inheritance from the Hermitian UQC case. The conditional unitary is a qubit-state-dependent basis change defined on the composite Hilbert space and can be introduced independently of whether the subsequent evolution operator is unitary. The dynamical invariant is then required to obey the Heisenberg equation, which yields algebraic constraints on the Hamiltonian coefficients; these constraints remain well-defined for non-Hermitian operators. The fidelity value is obtained by direct numerical integration of the resulting time-dependent evolution (or master equation) and comparison with the target cat state. In the revised manuscript we will add a dedicated paragraph that explicitly verifies the commutation relations and the preservation of the invariant form under the non-Hermitian Hamiltonian, thereby addressing the load-bearing concern. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies external UQC framework and Heisenberg constraints without reduction to inputs

full rationale

The paper invokes universal quantum control (UQC) theory to analyze the system in an ancillary picture via a conditional unitary transformation, then uses the Heisenberg equation on the dynamical invariant to constrain the time-dependent Hamiltonian. When the qubit starts in a balanced superposition, the bosonic mode evolves from vacuum to a large cat state. This chain relies on standard external theory rather than self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The target photon number (>120) and fidelity (>0.962) emerge from satisfying the derived constraints, not by construction from the target itself. No steps match the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The protocol depends on the existence and controllability of dynamical invariants in the ancillary picture and on the validity of mapping the Heisenberg equation directly to Hamiltonian constraints; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption System dynamics of hybrid qubit-bosonic systems can be analyzed in the ancillary picture via a unitary transformation conditional on the qubit state.
    This is the foundational step of the UQC analysis described in the abstract.
  • domain assumption The controllable dynamics encoded in the dynamical invariant can be presented by the Heisenberg equation, which imposes constraints on the Hamiltonian.
    Directly invoked to enable deterministic evolution to the cat state.

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discussion (0)

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Reference graph

Works this paper leans on

103 extracted references · 3 canonical work pages · 2 internal anchors

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    Deterministic generation of cat states with more than $100$ photons under dissipation

    2 [ 39]. Besides the two-legged cat states, the four-legged cat states or so-called compass states [ 24, 38, 40–46]: |α ⟩ + | −α ⟩ + |iα ⟩ + | −iα ⟩ are more promising candidates for quantum technologies, such as quantum metrology [ 43], dark matter searching [ 44], and quantum error tracking and correction in the presence of photon loss [ 38, 41, 42]. Re...

    work page internal anchor Pith review Pith/arXiv arXiv 2026

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    Here θ(t) and β (t) are time-dependent amplitude and phase, respectively

    takes a conditional form as V(t) = D†[α (t)] ⊗ |e⟩⟨e|+D[α (t)] ⊗ |g⟩⟨g|, (11) whereD[α (t)] ≡ exp[α (t)m† − α ∗ (t)m] is a displacement operator with α (t) = θ(t) exp[−iβ (t)]. Here θ(t) and β (t) are time-dependent amplitude and phase, respectively. In the rotating frame with respect to V(t) in Eq. ( 11), H(t) in Eq. ( 10) is transformed as Hrot(t) = V †...

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    Equation (

    (15) The constraint on the eigenfrequency of the qubit is re- laxed. Equation (

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    And using Eq

    suggests that the systematic pa- rameters inH(t) are not necessarily time-dependent, pro- vided thatθ(t) andβ (t) can be chosen as a linear function of time and constant, respectively. And using Eq. ( 15), Hrot(t) in Eq. ( 12) is reduced to Hrot(t) = ω m(t)m†m + ω q(t) 2 σz − ω m(t)θ2(t). (16) Then according to Eq. ( 3), the relevant dynamical invari- ant...

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    has to be modified with the displacement amplitudes that embody extra amplifi- cation or attenuation. Then we have ˜V(t) = D†[ ˜α (t)] ⊗ |e⟩⟨e|+D[ ˜α (t)] ⊗ |g⟩⟨g|, (21) where the time-dependent displacement operator is de- fined by D[ ˜α (t)] ≡ exp[ ˜α (t)m† − ˜α ∗ (t)m] with ˜α (t) = θ(t) exp[−iβ (t) − βi(t)]. θ(t), β (t), and βi(t) are time- dependent rea...

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    Using ˜Ae and ˜Ag, the linear terms of Hrot(t) in Eq

    and ( 14), respectively, under the replacements of ω m(t) → ˜ω m(t), ω q(t) → ˜ω q(t), and α (t) → ˜α (t). Using ˜Ae and ˜Ag, the linear terms of Hrot(t) in Eq. (22) can be neutralized by imposing the following constraints on the dynamical components: ω m(t) = ˙β (t) + γm 2 sinϕ m, g (t) = ˙θ(t)e− β i(t), ϕ =β (t) + π 2, γ m cosϕ m = − 2 ˙βi(t), (23) unde...

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    0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50(a) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 120 140(b) FIG

    or ( 20) and contributes to the probability nonconservation of the system wave-function. 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50(a) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 120 140(b) FIG. 3. Dynamics of the density-matrix trace about the whole system Tr[ρ(t)], the fidelity F(t) with respect to the target state |Ψ(τ)⟩ = ( ...

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    The longitudinal coupling strength is larger than the gain or loss rates by one order in magnitude

    142λ 1,θ(t) = 7πt/ 2τ. The longitudinal coupling strength is larger than the gain or loss rates by one order in magnitude. g/γ m ∼ 10 for t ∈ [0,τ/ 2] and g/γ m ∼ 20 for t ∈ [τ/ 2,τ ]. To save the probability conservation at the target mo- ment t = τ, the whole evolution can be parameterized to two stages as (i) t1 ∈ [0,τ/ 2] and (ii) t2 ∈ [τ/ 2,τ ]. Duri...

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    and ( 25), at the turning point t = τ/ 2, the sudden switching from the gain ef- fect to loss effect (or vice versa) can be realized by a sudden change in βi(t). Despite the parameters might be non-differentiable, however, the system dynamics pre- sented by the dynamical invariant is required to be con- 7 tinuous around the vicinity of the tuning point. Thu...

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    For the composite system initially in the state |ψ (0)⟩ = |0⟩ ⊗ | +⟩, it will evolve to a highly entangled cat state at t = τ

    can be simplified as |exp(−λ 1θ(τ− / 2)) − exp(−λ 2θ(τ+/ 2))|2 ≈ 0, which is always attainable under appropriate choices of λ 1 andλ 2. For the composite system initially in the state |ψ (0)⟩ = |0⟩ ⊗ | +⟩, it will evolve to a highly entangled cat state at t = τ. The gain or loss rate of the qubit is set as γτ = 0. 5 with ϕ q = 0 when t ∈ [0,τ/ 2] and ϕ q =...

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    In the rotating frame with respect to the conditional unitary transformation ˜V(t), obtained by Eq

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    ( 30) are of the comparable order in magnitude to those in Fig

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    is found to be µ (0) = |0⟩⟨0| ⊗ |ee⟩⟨ee|+ |0⟩⟨0| ⊗ |gg⟩⟨gg| + |0⟩⟨0| ⊗ |eg⟩⟨eg|+ |0⟩⟨0| ⊗ |ge⟩⟨ge|. (40) And in the original picture it evolves as µ (t) = ˜V(t)µ (0) ˜V †(t) = | − ˜α (t)⟩⟨− ˜α (t)| ⊗ |ee⟩⟨ee| + |˜α (t)⟩⟨˜α (t)| ⊗ |gg⟩⟨gg|+ | −i ˜α (t)⟩⟨−i ˜α (t)| ⊗ |eg⟩⟨eg| + |i ˜α (t)⟩⟨i ˜α (t)| ⊗ |ge⟩⟨ge|. (41) under the inversion of V(t) in Eq. ( 37). ...

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