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arXiv:2512.23323

Generation of Squeezed Fock States by Particle-Number Measurements on Multimode Gaussian States

S. B. Korolev, A. A. Silin

quant-phSubmitted Dec 29, 2025• Announced Dec 30, 2025• 0 citations
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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.

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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.
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.
Subject of study. Schemes for generating non-Gaussian quantum states and the states required for quantum error correction protocols are investigated. Aim of study. The primary objectives were to generalize methods and approaches for describing the generation of non-Gaussian states in measurement schemes to determine the most effective model for describing the generation process and to assess a model for generating squeezed Fock states and a quantum error correction code based on such states. Method. A theoretical analysis of the wavefunction evolution of various non-Gaussian states in particle-number measurement schemes was performed; in this analysis, squeezed states were used as inputs. Main results. A scheme for generating squeezed Fock states was theoretically examined. An explicit analytical expression for the output wavefunction was constructed to completely analyze the output states depending on the parameters of the scheme under consideration. A set of conditions imposed on the parameters of a two-mode entangled Gaussian state, i.e., the “universal solution regime,” was outlined. This regime guaranteed the generation of squeezed Fock states with a high probability. Practical significance. The results demonstrated the ability of the universal solution regime to generate squeezed Fock states of arbitrary order for a given squeezing parameter. The feasibility of using squeezed Fock states in quantum error correction codes was analyzed. A comparative study of squeezed Fock states and squeezed Schrödinger cat states as codewords confirmed squeezed Fock states as robust solutions to ensure information protection in channels subjected to particle loss and dephasing.
Generation of highly non-classical quantum states of light is essential for optical quantum information processing and quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic quantum-state engineering schemes represents one of the central challenges in current quantum optics. As technology advances and experiments progress to detection of higher numbers of photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional quantum state preparation schemes based on Gaussian states and photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined photon number parity. We illustrate our general methodology through examples of generation of single-mode states with two and three heralding modes, and generation of two-mode states with two heralding modes.
The generation of squeezed Fock states by the one or more photon subtraction from a two-mode entangled Gaussian (TMEG) state is theoretically addressed. We showed that an arbitrary order Fock state can be generated this way and we obtained a condition that should be imposed on the parameters of the TMEG state to guarantee such a generation. We called the regime, in which this condition is satisfied, the universal solution regime. We showed that, for the first squeezed Fock state, the above condition is redundant such that the generation of the first squeezed Fock state is still possible by a one-photon subtraction from an arbitrary TMEG state. At the same time, the maximum generation probability of the first squeezed Fock state generation corresponds to the universal solution regime. We applied the above results to the description of generation of the squeezed Fock states using a beam splitter and a controlled-Z operation. We have estimated the parameters of such setups and input squeezed states, which are necessary to obtain squeezed Fock states with the maximum probability.