Deterministic feedforward-based generation of large optical coherent-state superposition

arXiv:2603.22068 · quant-ph · Submitted 2026-03-23 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Deterministic feedforward-based generation of large optical coherent-state superposition".

Mira: The gist Large optical coherent-state superpositions are essential to advance quantum sensing, quantum repeaters and error-correction codes.

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, we've seen that this paper is tackling how to make these large optical cat states deterministically. They introduce a deterministic feedforward protocol that uses qubit-mode dispersive coupling to achieve this.

Mira: The core of what they claim is that their single-mode protocol outperforms the advanced three-mode Gaussian photon-number resolving detector scheme in terms of average fidelity and quantum non-Gaussian phase space properties.

Lev: That's a big claim because the benchmark method has these limitations, right? It can only conditionally project a Gaussian state onto a finite superposition of Fock states of rank less than or equal to 2n, which limits the success rate significantly when you want large cat amplitudes <ref:2603.22068#pg1>.

Kai: Right, and this paper is addressing that limitation by exploiting light-atom interaction to translate the superposition created in the qubit into the optical mode.

Mira: They also propose a way to guarantee even parity of the output state by choosing a balanced second beam splitter with pi phase shifts, which simplifies their free parameters p to just r1, r2, r3 and T.

Lev: So for someone building hardware, that means they're trying to keep the required components simple while still achieving this deterministic generation of large states.

Kai: And they show in Figure three oscillations of the Wigner function along the y axis for both protocols, with n equals one and two showing how much more powerful the dispersive protocol is for generating large cat amplitudes <ref:2603.22068#pg3,Figure 3 oscillations of the Wigner function along the y axis for>.

Mira: They also look at robustness against imperfect realization, modeling losses as a beam splitter with transmissivity tau less than or equal to one and they find that the dispersive fidelity FD(tau) loses its asymptotic behavior there <ref:2603.22068#pg1>.

Lev: That means if you have actual optical losses in the setup, the ideal performance curve you see doesn't hold anymore; it turns into a decreasing function that scales as e to the power of negative alpha squared times one minus root tau squared plus e to negative two alpha squared times one minus tau squared plus a constant term.

Kai: So, even with some losses, they still provide a more robust quantifier for the quality of large cat states by looking at the minimum resolvable displacement.

Mira: In short, the paper argues that combining cavity QED experiments with well-established electro-optical feedforward methods gives us a deterministic way to generate these states that is more effective than current three-mode Gaussian detection schemes.

Conclusion: Kai: Thinking about the title, 'Deterministic feedforward-based generation of large optical coherent-state superposition', it really captures the essence: taking a process that is usually probabilistic and making it deterministic using feedforward techniques.

Mira: The authors, Notarnicola, Jarzyna, and Filip, are combining cavity QED with electro-optical methods to achieve this specific goal for generating these large states.

Lev: For the broader community building hardware, what does this protocol mean in terms of what it takes to actually run something like this on a real quantum computer or a lab setup?

Kai: Well, it means they're using dispersive coupling that is already available in QED setups, and then adding an electro-optical feedforward step to make the output deterministic.

Mira: The implication for us is that this approach isn't just theoretical; it suggests we can build systems where we are not limited by the success probability of generating states with large cat amplitudes.

Lev: If you can achieve deterministic generation, you shift the focus from maximizing success rate to actually controlling the state properties, which is a huge part of error correction and sensing.

Kai: Exactly. And they extend this protocol to unbalanced cat states, squeezed cat states, and even multi-headed cat states for phase sensing applications.

Mira: So what we're looking at here is a deterministic tool that can be translated across different platforms, from optical to microwaves or even atomic ensembles in the future.

Lev: If this works out as described with the fidelity scaling and robustness against losses, it gives us a viable path toward realizing these large superpositions for things like quantum repeaters or error-correction codes.

Kai: It's about combining established QED techniques with feedforward to engineer states that are better characterized and more useful for real-world quantum applications.

Department of Optics, Palacky University · Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw

quant-ph

Submitted: 2026-03-23

Updated: 2026-10-20

Comments: Main text: 6 pages, 4 figures SM: 15 pages, 10 figures

Journal ref: Phys. Rev. Research 8, 043068 (2026)

DOI: 10.1103/l944-5x1g

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 81/100

The gist: The gist Large optical coherent-state superpositions are essential to advance quantum sensing, quantum repeaters and error-correction codes.

Key concepts

Qubit-Mode Dispersive Coupling: This technique uses the interaction between a single atom (qubit) embedded in an optical cavity and light fields. It is realized by reflecting an optical pulse off the cavity, creating a dispersive interaction that links the atomic state to the light's properties. This coupling forms the basis for generating entangled states between atoms and photons.
Deterministic Feedforward Protocol: This is a process where measurements of one part of an experiment immediately trigger a corrective action on another part. In this case, if a specific measurement outcome is observed, the system automatically applies a precise displacement operation to the light state. This makes the generation of complex states like large cat states reliable and predictable.
Gaussian-Photon-Number-Resolving Detector: This is an advanced detection scheme used to measure the quantum properties of light states by resolving photon numbers within a Gaussian envelope. The proposed dispersive protocol is shown to be superior to this method because it achieves better average fidelity and preserves more desirable non-Gaussian phase space features for larger superpositions.
Quantum Non-Gaussian (QNG) Phase Space Properties: These are specific mathematical characteristics of the quantum state's phase space that distinguish it from simple, classical states. The paper shows that the proposed protocol generates these desired QNG properties more effectively than conventional methods, which often only reproduce a finite rank of these features.

Terminology

Fidelity — 1× in this paper · explained in 2 episodes
Quantum Interference — 1× in this paper · explained in 3 episodes
Quantum sensing — 1× in this paper · explained in 2 episodes

Summary

The gist Large optical coherent-state superpositions are essential to advance quantum sensing, quantum repeaters and error-correction codes. This paper proposes a deterministic feedforward protocol employing qubit-mode dispersive coupling to generate large optical coherent-state superpositions that outperform advanced three-mode Gaussian-photon-number-resolving detector schemes in terms of average fidelity and quantum non-Gaussian phase space properties

Conventional Methods Limitations

Conventional methods for generating optical cat states adopt probabilistic schemes based on either photon subtraction or addition, which are associated with two main limitations. Firstly, they are efficient only for kitten generation, as they implement conditional projection over a finite superposition of Fock states embedded in a Gaussian envelope. In turn, generation of cats with α ≥ 2 becomes challenging, requiring a large number of heralded photons to achieve high fidelity and, moreover, quantum non-Gaussian (QNG) phase space properties, thus inducing a significant drop of the success rate. Even if cat enlargement protocols have also been proposed, they come at the cost of further reduction of success probability. Secondly, QNG interference properties of the resulting states are only partially reproducing the desired ones, as they only get finite stellar rank.

Deterministic Dispersive Protocol

The proposed deterministic single-mode feedforward protocol is based on dispersive coupling [Fig. 1(a)], obtained by embedding the single-atom cavity in a Gaussian electro-optical feedforward with advantages to (a) Dispersive cavity QED feedforward protocol and (b) Benchmark: nonlinear optics GP(2n) heralded protocol three-mode Gaussian state preparation. The dispersive interaction is realized on traveling waves thanks to reflection of an optical pulse from a cavity containing a single Λ-type atom in the limit of large cooperativity. The protocol involves applying a π/2 pulse onto a coherent state of radiation iα⟩, α ≥ 0, and atomic state +⟩ = (g⟩ + e⟩)/√2 to create the “atom-light entangled state” ΨD⟩ = (g⟩α⟩ + e⟩ − α⟩)/√2. Subsequent qubit measurement in the basis is used such that if “+” is retrieved, light is projected exactly into the target state ψcat (+)⟩, whereas in the opposite case we obtain the orthogonal odd cat. To make it deterministic, when outcome “-” is registered we apply a feedforward displacement operation D(±iγ), γ ≥ 0 on the optical state, whose sign is randomly chosen with 50% probability, inducing either positive or negative shift of the interference fringes along the y direction of phase space.

Performance Comparison and Scaling

The dispersive protocol achieves much better performance than the benchmark GP(2n) scheme for large cat generation in essential quantum features. For large α, FD becomes an increasing function that asymptotically approaches 1 as FD ≈ 1−π/2/32α squared for α >> 1. This provides comparable results to the protocol for microwave cats generation proposed in [41] whose fidelity scales as ≈ 1−π/2/64α squared, that however, requires sequential iterations of dispersive couplings whereas our proposal only needs a single light-atom interaction step, being assisted by Gaussian feedforward. The success probability for the GP(2n) scheme for α >> 1 approaches ≈ 5%,0.19%,0.13% for n = 1,2,3.

Robustness to Imperfect Realization and Decoherence

The analysis investigates robustness against additional losses modeled as a beam splitter with transmissivity τ ≤ 1. In the dispersive protocol, the average output mixture is given by ρD(τ) = p+ρ+(τ) + p−/2 hρ′(τ; γD) +ρ′(τ;−γD) i, where FD(τ) loses the asymptotic behavior of the ideal state preparation case even in the presence of minuscule losses, being turned into the decreasing function: FD(τ) ≈ e−α squared (1−√τ) squared 1+e−2α squared (1−τ) squared 1−π/32α squared for α >> 1. Furthermore, the minimum resolvable displacement provides a more robust quantifier of large cat-state quality.

Quantum Fisher Information Analysis

The quantum Fisher information (QFI) provides the ultimate precision limits compatible with quantum mechanics laws for a probe state ρ0 = ∑n ρnϕn⟩⟨ϕn, where ˆx = (a+a†)/√2 is the position-like operator. For the target cat states ψcat (+)⟩, homodyne detection provides the optimal measurement strategy, with sensitivity εε(+)cat = 1/2 s 1+4α squared 1±e−2α squared. In the limit α >> 1, homodyne detection approaches the optimal detection strategy so that eεD ≈ εD.

Conclusion on Applicability

The proposed protocol can be straightforwardly extended to target a wider class of superposition states, including unbalanced cat states ψ⟩ ∝ c1α⟩ + c2 − α⟩ relevant for phase sensing, squeezed cat states S(r)ψcat (±)⟩, and multi-headed cat states. The proposed protocol can also be translated to other platforms, including microwaves [41, 63–66], atomic ensembles [67, 68] and mechanical modes [69–72].

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Improvements for AI systems

The AI system can deterministically generate large optical coherent-state superpositions, such as even cat states ψcat(±)p⟩, by employing a deterministic feedforward protocol employing qubit-mode dispersive coupling. This allows for state preparation beyond the limitations of probabilistic schemes like photon subtraction or addition.
The system can outperform benchmark protocols like the Gaussian-PNRD scheme for large cat generation, achieving high average fidelity and required quantum non-Gaussian (QNG) interference fringes in phase space, as shown by the result that dispersive interaction provides a deterministic scheme that outperforms GP(2n) in the limit of large α.
The AI system can be robust against experimental imperfections, specifically imperfect dispersive coupling and qubit detection decoherence, maintaining performance even when these noise sources are present. For example, the fidelity remains an increasing function of the target cat amplitude in the large amplitude regime: "F(pd)D ≈ 1+e−λ2/32α2 for α >> 1."
The system can serve as a reliable witness of quantum interference by quantifying displacement sensitivity, which is shown to be a more robust quantifier of large cat-state quality than fidelity or Wigner negativity: the minimum resolvable displacement provides a more robust quantifier of large cat-state quality.