A new class of pure non-Gaussian quantum states

arXiv:2607.11774 · quant-ph · Submitted 2026-07-13 · 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: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "A new class of pure non-Gaussian quantum states".

Kai: The gist A new class of pure non-Gaussian quantum states characterized by trigonal symmetry on the phase plane is proposed,

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

Title and authors: Mira: The paper, "A new class of pure non-Gaussian quantum states," was written by V. L. Gorshenin, B. N. Nougmanov, D. A. Chermoshentsev, I. A. Bilenko, and F. Ya. Khalili in the introduction to set the stage for this work on new quantum states characterized by trigonal symmetry on the phase plane #pg1

Kai: That title hints at something new they've found about how light behaves in these complex systems, moving beyond just standard Gaussian states we usually deal with in continuous variable setups.

Mira: They are proposing a specific mathematical structure for these non-Gaussian states, which is their term "trigonal states," and showing that they can actually be generated through a process called non-degenerate four-wave mixing combined with heralding.

Lev: So what this means for the practical side is that they aren't just describing a theoretical construct; they are showing a pathway to create these states experimentally using techniques we already have, which is good news for testing them out.

Kai: That's the point. It bridges the gap between theory and experiment by providing a clear recipe—the four-wave mixing plus photon number measurement—to access these new state types.

The paper's summary: Kai: In terms of what they actually did, they model a four-mode optical system where the pump modes are treated classically, and they simplify the full Hamiltonian down to two main parts that describe standard squeezing and parametric interactions #pg2

Mira: They then look at the evolution operator over time, using a perturbative approach where one part describes simple squeezing and the other part describes those interactions between different modes #pg3

Kai: The result of looking at how the system evolves is that when you start with vacuum states for both signal modes, this process leads to a specific form for the unperturbed evolution and then a perturbation term that looks like it creates entanglement.

Lev: The paper shows that this evolution results in a final two-mode quantum state which they decompose into a standard two-mode squeezed state and some perturbation term #pg2

Kai: And from that decomposition, they derive an explicit expression for the final heralded state, psi out, and that's where the core finding is—it has this hidden trigonal symmetry.

Mira: They characterize this symmetry by saying that only certain quantum levels with numbers n = n0 + 3k are occupied in the final state, which really defines what makes it a trigonal state.

The paper's improvements: Kai: The authors suggest a few ways to take this idea further, focusing on how these states can be used in real applications for quantum information processing and sensing.

Mira: One major improvement is that because of this inherent symmetry, you can engineer quantum states that are invariant under specific unitary transformations, like rotating both modes by two pi/three degrees #pg1 <ref:2607.11774#pg3>

Lev: That would be very useful for building robust algorithms because if the state has that symmetry, it's more resilient to certain types of noise or phase errors that would otherwise mess up a less symmetric state.

Kai: Right. The second improvement is using this symmetry for quantum sensing and metrology, where you can characterize the states based on these specific occupation patterns #pg2

Mira: Specifically, the paper suggests that because only those levels with n = n0 + 3k are occupied, you can perform highly sensitive measurements using photon number detection to leverage this structure.

Lev: If we translate that to hardware, it means we don't need an impossibly complex measurement setup just to characterize the state; you target these specific occupation numbers directly.

Conclusion: Kai: So, wrapping up on "A new class of pure non-Gaussian quantum states," the main thing is that they've shown a way to generate states with trigonal symmetry using four-wave mixing and heralding, leading to these highly structured quantum states.

Mira: The implication is that this isn't just a theoretical curiosity; it gives us a new class of non-Gaussian states we can potentially prepare, which opens up doors for more sophisticated quantum information processing and sensing applications.

Lev: For running this on actual hardware, the main challenge will be implementing the photon number measurement reliably enough to extract that specific symmetry you mentioned #pg2

Kai: Right, so it's about building a reliable way to measure those modes in a four-wave mixing setup to access these states.

Mira: And that’s what we’re focusing on next, exploring how these concepts interact with other areas of condensed matter physics and quantum materials.

Lev: We'll see if this symmetry holds up when we look at more complex systems like the nickelates or cuprates that we've been studying recently #pg1

Russian Quantum Center · Moscow Institute of Physics and Technology

quant-ph

Submitted: 2026-07-13

Updated: 2026-10-08

Comments: 6 pages, 5 figures, 1 table

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

Importance score: 64/100

The gist: The gist A new class of pure non-Gaussian quantum states characterized by trigonal symmetry on the phase plane is proposed, generated using standard non-degenerate four-wave mixing supplemented by a

Key concepts

Non-Gaussian Quantum States: These are quantum states that cannot be described by simple Gaussian states. They are important because they test the limits of quantum physics in macroscopic systems and are crucial for advanced tasks like quantum communication and computing, although they are difficult to create.
Four-Wave Mixing (FWM): This is a process where four optical waves interact to generate new light waves. In this study, FWM was used as the mechanism to generate the desired non-Gaussian quantum states by coupling different modes in an optical system.
Trigonal Symmetry: This refers to a specific type of rotational symmetry in the state's phase plane. The paper shows that the generated quantum state possesses this hidden symmetry, meaning its properties are constrained in a way that only certain photon number levels can be present.

Terminology

Quantum Physics — 3× in this paper · explained in 10 episodes
Entanglement — 2× in this paper · explained in 3 episodes
Wigner function — 2× in this paper · explained in 2 episodes
Core — 1× in this paper · explained in 2 episodes

Summary

The gist A new class of pure non-Gaussian quantum states characterized by trigonal symmetry on the phase plane is proposed, generated using standard non-degenerate four-wave mixing supplemented by a heralded measurement of photon number in one signal mode.

Introduction

Non-Gaussian quantum states are of significant interest for various fields including fundamental tests of applicability of quantum physics to macroscopic objects, quantum interferometry, and quantum information processing and communications Unfortunately, non-Gaussian quantum states are hard to prepare and vulnerable to dissipation, readily decaying into non-coherent mixes of Gaussian states. For now, only two classes of pure non-Gaussian states, namely Fock states and Schrodinger cat ones, can be prepared more or less reliably. In the classical domain, optical bistability arising during spontaneous degenerate parametric generation can be considered as an analog of the Schrodinger cat generation process. Recently, it was demonstrated experimentally that in more sophisticated setups with non-degenerate (two-component) pumping, multistable solutions with the axial symmetry of order n > 2 also exist. In the quantum case, all branches of evolution in these multistable systems will coexist, leading to the kind of “mutlihead cat states”.

The System

The system considered is a four-mode optical system shown in Fig. 1. The annihilation operators for the signal and pump modes are denoted by the symbols ˆa1,2 and ˆb1,2 respectively, with all of them being equidistant. The pump modes are assumed to be classical ones, described by bˆ1,2 → βe iϕ1,2, where β ≫ 1 is the amplitude and ϕ1,2 are the phases of these modes. The full Hamiltonian of this system can be significantly simplified by neglecting self phase modulation (SPM) and cross phase modulation (XPM) effects imposed by the pump modes, as they can be taken into account in some way.

The remaining Hamiltonian is given by Hˆ = Hˆ 0 + Hˆ 1.

Hˆ 0 = ħγa†1 a†2 e i(ϕ1+ϕ2) + h.c. (3a) is the standard bilinear two-mode-squeezing Hamiltonian.

Hˆ 1 = ħκ(a†1/2 a squared e iϕ1 + a†2/2 a 1 e iϕ2) + h.c. (3b) originates from the degenerate parametric interactions of the modes bˆ1, ˆa1, ˆa2 and bˆ2, ˆa2, ˆa1 respectively. The coupling constant relation is κ/γ∝ β-1≪ 1. The annihilation operators are further simplified by replacing a†i:= a†i exp i(2ϕi + ϕj) for i=1,2 and j=3. This leads to the simplified Hamiltonians Hˆ 0 = ħγa†1 a†2 + h.c. (6a) and Hˆ 1 = ħκ(a†1/2 a squared + a†2/2 a 1) + h.c. (6b).

Evolution of the System

The evolution operator Uˆ (t) of the system is governed by iħ dUˆ (t)/dt = HˆUˆ (t). The evolution operator is presented as Uˆ (t) = Uˆ 0(t)Uˆ 1(t). The unperturbed part evolves as Uˆ 0 (t) = e-iγt(a†1 a†2 + a 1 a 2). The perturbation evolution is given by Hˆ 1(t) = Uˆ† 0(t)Hˆ 1Uˆ 0(t) = ħκ[a†1/2 (t)a 2(t) + a†2/2 (t)a 1(t)] + h.c.

For the case where both signal modes are initially in the vacuum states 0⟩1,2, the solution to Eq. (10) in the linear approximation is found to be Uˆ 1(t) = 1 + ∫ t0 t Hˆ 1 (t') dt'. This results in a term for Hˆ 1 (t)0⟩1 ⊗ 0⟩2 of the form-ħκ(i cosh2γt sinh γt + cosh γt sinh2γt) (a†1/3 + a†2/3)0⟩1 ⊗ 0⟩2.

Heralded State

The final two-mode quantum state is presented as Ψ⟩ = Uˆ (t)0⟩1 ⊗ 0⟩2 = Uˆ 0(t) [ˆI + δUˆ 1(t)Uˆ† 0(t)] 0⟩1 ⊗ 0⟩2. This state is decomposed into a two-mode squeezed state S2⟩ and a perturbation term δΨ⟩. The two-mode squeezed state is given by S2⟩ = Uˆ 0(t)0⟩1 ⊗ 0⟩2 = 1/cosh γt ∑n=0 g n(t)n>1 ⊗ n>2 with g(t) = -i tanh γt. The perturbation term is given by δΨ⟩ = Uˆ 0(t)δUˆ 1(t)Uˆ† 0(t)S2⟩.

The state Ψ⟩ can be expressed in terms of the basis states as Ψ⟩ = 1/cosh γt ∑n=0 g n(t)n>1⊗n>2 + κγ K(γt) cosh3γt √ (n+1)(n+2)(n+3) (n+3⟩1 n>2 + n>1 n+3⟩2. The corresponding normalized heralded state of the first signal mode, obtained by measuring the photon number "m" of the second mode, is ψout⟩ = m>1 + ψ+3m+3>1 + ψ-3m-3>1. This state possesses a hidden trigonal symmetry, as rotation of both modes to opposite directions by the same angle 2π/3 corresponds to applying the evolution operator exp 2πi/3(nˆ1-nˆ2). The occupation probabilities show that only quantum levels with the numbers n = n0 + 3k, where n0 and k are integer numbers, are occupied, which characterizes the trigonal symmetry.

Conclusion

This work considered only the simplest case of multimode quantum systems interacting by means of the four-wave mixing process. The symmetries of order n + 1 could exist in the case of n interacting modes, leading to very non-trivial and interesting quantum states that are worth exploring.

Acknowledgments

This work was supported by the Russian Science Foundation (project number 25-12-00263). The references listed are [1] S. L. Braunstein and P. van Loock, Quantum information with continuous variables, Rev. Mod. Phys. 77, 513 (2005) <ref:2607.

Improvements for AI systems

textbfFundamental Symmetry-Preserving State Preparation for Quantum Information Processing: The trigonal symmetry of heralded states can be used to engineer quantum states invariant under specific unitary transformations, such as rotation of both modes to opposite directions by the same angle 2pi/3, which is crucial for developing robust quantum algorithms that are resilient to certain types of noise or phase errors.
textbfEnhanced Quantum Sensing and Metrology: The resulting heralded state, described by Eq. (27), possesses a hidden trigonal symmetry, allowing it to be characterized by the occupation pattern where only the quantum levels with the numbers n = n0 + 3k, where n0 and k are integer numbers, are occupied, enabling highly sensitive measurements based on photon number detection that leverage this specific symmetry.
textbfModel Validation and Parameter Estimation: The analytical model for the heralded state (25) provides a benchmark against numerical simulations (Fig. 3), allowing AI systems to rapidly estimate system parameters like the squeezing parameter g(t) or the interaction strength κ, which is vital for optimizing experimental setups involving four-wave mixing processes.