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arXiv:2609.00343

Generation of multicomponent Schrödinger cat states in schemes with measurement of Gaussian states

E. A. Nesterova, S. B. Korolev

quant-phSubmitted Aug 31, 2026• Announced Sep 2, 2026• 0 citations
v1 · Aug 31, 2026v2 · Sep 9, 2026
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Abstract

In this work, we propose a scheme for generating superpositions of Fock states whose numbers differ by four or eight. The proposed protocol is based on photon-number-resolving measurements on multimode Gaussian states. We compare of the generated states with multicomponent Schrödinger cat states. We evaluate the fidelity and determine how it scales with the number of detected particles. Furthermore, we derive the optimal configuration for the generation such states.

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In this work, we propose a scheme for generating superpositions of Fock states whose numbers differ by four or eight. The proposed protocol is based on photon-number-resolving measurements on multimode Gaussian states. We compare of the generated states with multicomponent Schrödinger cat states. We evaluate the fidelity and determine how it scales with the number of detected particles. Furthermore, we derive the optimal configuration for the generation such states.
In this work, we investigate the generation of squeezed Schrödinger cat states in schemes based on photon-number-resolving measurements on multimode Gaussian states. We derive analytical expressions for the states generated in two- and three-mode schemes, as well as formulas for their fidelity with squeezed Schrödinger cat states. We analyze how the amplitude of the generated states scales with the number of detected particles. Furthermore, we derive an upper bound on the achievable generation fidelity and identify the conditions under which multimode schemes can enhance the quality of the generated states.
We investigate the generation of squeezed Fock states (SFSs) via particle-number measurements in the modes of multimode Gaussian states. We identify a universal class of NNN-mode Gaussian states for which measuring N−1N-1N−1 modes results in the generation of SFSs. The key feature of these states is that the generated SFSs depend only on the total number of detected particles and are independent of their distribution among the detectors. Based on the general form of the wave functions of multimode Gaussian states, we propose a universal scheme for SFS generation. For this scheme, we evaluate the probability of SFS generation and analyze the robustness of the process against imperfections in particle-number-resolving detectors. In addition, we compare the universal scheme with a nonuniversal scheme, in which the generation of SFSs depends on a specific distribution of particle numbers across the detectors. We demonstrate that the universal scheme provides a higher probability of SFS generation, at the cost of increased experimental resources.
Abstract We investigate the generation of squeezed Fock states (SFSs) via particle-number measurements in the modes of multimode Gaussian states. We identify a universal class of N -mode Gaussian states for which measuring N − 1 modes results in the generation of SFSs. The key feature of these states is that the generated SFSs depend only on the total number of detected particles and are independent of their distribution among the detectors. Based on the general form of the wave functions of multimode Gaussian states, we propose a universal scheme for SFS generation. For this scheme, we evaluate the probability of SFS generation and analyze the robustness of the process against imperfections in particle-number-resolving detectors. In addition, we compare the universal scheme with a nonuniversal scheme, in which the generation of SFSs depends on a specific distribution of particle numbers across the detectors. We demonstrate that the universal scheme provides a higher probability of SFS generation, at the cost of increased experimental resources.
We present a detailed analytic framework for studying multimode non-Gaussian states that are conditionally generated when few modes of a multimode Gaussian state are subject to photon-number-resolving detectors. From the output state Wigner function, we deduce that the state factorizes into a Gaussian gate applied to a finite Fock-superposition non-Gaussian state. The framework provides an approach to find the optimal strategy to generate a given target non-Gaussian state. We explore examples, such as the generation of cat states, weak cubic phase states, and bosonic code states, and achieve improvements of success probability over other schemes. Our framework also applies to the case in which the measured Gaussian state is mixed which is very important for the analysis of experimental imperfections such as photon loss. The framework has potential far-reaching implications to the generation of bosonic error-correcting codes and for the implementation of non-Gaussian gates using resource states, among other applications requiring non-Gaussianity
Optical Schrödinger cat states are non-Gaussian states with applications in quantum technologies, such as for building error-correcting states in quantum computing. Yet the efficient generation of high-fidelity optical Schrödinger cat states is an outstanding problem in quantum optics. Here, we propose using squeezed superpositions of zero and two photons, ∣θ⟩=cos⁡(θ/2)∣0⟩+sin⁡(θ/2)∣2⟩|θ\rangle = \cos{(θ/2)}|0\rangle + \sin{(θ/2)}|2\rangle∣θ⟩=cos(θ/2)∣0⟩+sin(θ/2)∣2⟩, as ingredients for protocols to efficiently generate high-fidelity cat states. We present a protocol using linear optics with success probability P≳50%P\gtrsim 50\%P≳50% that can generate cat states of size ∣α∣2=5|α|^2=5∣α∣2=5 with fidelity F>0.99F>0.99F>0.99. The protocol relies only on detecting single photons and is remarkably tolerant of loss, with 2%2\%2% detection loss still achieving F>0.98F>0.98F>0.98 for cats with ∣α∣2=5|α|^2=5∣α∣2=5. We also show that squeezed θθθ states are ideal candidates for nonlinear photon subtraction using a two-level system with near deterministic success probability and fidelity F>0.98F>0.98F>0.98 for cat states of size ∣α∣2=5|α|^2=5∣α∣2=5. Schemes for generating θθθ states using quantum emitters are also presented. Our protocols can be implemented with current state-of-the-art quantum optics experiments.
Generation of high-fidelity photonic non-Gaussian states is a crucial ingredient for universal quantum computation using continuous-variable platforms, yet it remains a challenge to do this efficiently. We present a general framework for a probabilistic production of multimode non-Gaussian states by measuring a few modes of multimode Gaussian states via photon-number-resolving detectors. We use Gaussian elements consisting of squeezed displaced vacuum states and interferometers, the only non-Gaussian elements consisting of photon-number-resolving detectors. We derive analytic expressions for the output Wigner function, and the probability of generating the states in terms of the mean and the covariance matrix of the Gaussian state and the photon detection pattern. We find that the output states can be written as a Fock-basis superposition state followed by a Gaussian gate, and we derive explicit expressions for these parameters. These analytic expressions show exactly what non-Gaussian states can be generated by this probabilistic scheme. Further, it provides a method to search for the Gaussian circuit and measurement pattern that produce a target non-Gaussian state with optimal fidelity and success probability. We present specific examples such as the generation of cat states, ON states, Gottesman-Kitaev-Preskill states, NOON states, and bosonic-code states. The proposed framework has potentially far-reaching implications for the generation of bosonic error-correction codes that require non-Gaussian states and resource states for the implementation of non-Gaussian gates needed for universal quantum computation, among other applications requiring non-Gaussianity. The tools developed here could also prove useful for the quantum resource theory of non-Gaussianity.