Squeezed Fock states: Generation and application

Bashmakova E.N., Korolev S.B., Zinatullin E.R., Golubev Y.M., Golubeva T.Y.

For Russian citation (Opticheskii Zhurnal):

Башмакова Е.Н., Королев С.Б., Зинатуллин Э.Р., Голубев Ю.М., Голубева Т.Ю. Сжатые состояния Фока: генерация и применение // Оптический журнал. 2025. Т. 92. № 3. С. 89–103. http://doi.org/10.17586/1023-5086-2025-92-03-89-103

Bashmakova E.N., Korolev S.B., Zinatullin E.R., Golubev Y.M., Golubeva T.Yu. Squeezed Fock states: Generation and application [in Russian] // Opticheskii Zhurnal. 2025. V. 92. № 3. P. 89–103. http://doi.org/10.17586/1023-5086-2025-92-03-89-103

For citation (Journal of Optical Technology):

Abstract:

Subject of study. Schemes for generating non-Gaussian quantum states and quantum states required for quantum error correction protocols. Aim of study. Generalization of methods and approaches for describing the generation of non-Gaussian states in measurement schemes, determination of the most effective model for describing the generation process. Generalization of methods and approaches to the description of the generation of non-Gaussian states in circuits with measurements and identification of the most effective model for describing the generation process, as well as consideration of the model for generating compressed Fock states and the error correction code for quantum computing based on such states. Evaluation of a model for generating squeezed Fock states and a quantum error correction code based on such states. Method. A theoretical analysis of the evolution of the wave function of various non-Gaussian states in the particle number measurement schemes. Squeezed states are used as an input. Main results. A scheme for generating squeezed Fock states is theoretically addressed. Construction of an explicit expression for the output wave function is demonstrated. It allows for a complete analysis of output states depending on the parameters of the schemes under consideration. A set of conditions on the parameters of a two-mode entangled Gaussian state, the so-called "universal solution regime", is discussed. This condition guarantees the generation of the squeezed Fock states with a high probability. Practical significance. It is shown that the "universal solution regime" provides for the generation of an arbitrary order number of squeezed Fock states for a given squeezing parameter. The possibility of using squeezed Fock states in quantum error correction codes is considered. A comparative analysis of squeezed Fock states and squeezed Schrödinger cat states as codewords is carried out. It has been demonstrated that squeezed Fock states are quite competitive for protecting information in a channel with particle loss and dephasing.

Keywords:

squeezed Fock states, squeezed Schrödinger cat states, non-Gaussian states, bosonic error correction codes, quantum state engineering

Acknowledgements:

OCIS codes: 270.0270, 270.6570, 270.1670, 000.6800, 000.2700

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