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Advanced Quantum Technologies

Superposition of Squeezed States

Sheng-Chuan Tang, Yue Zhang

Published Jun 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Inspired by the superposition of coherent states, we investigate the superposition of squeezed states (pure Gaussian states) and propose a mathematical characterization under the Fock‐Bargmann representation, with the possibility to further generalize to the superposition of non‐Gaussian states. We introduce generalized circular states constructed by superposing squeezed coherent states symmetrically on a circle. We demonstrate their photon distributions as “trimmed and rescaled” versions of those of the initial squeezed states. We find that squeezing disappears while higher‐order squeezing might be strengthened for some specific generalized circular states. We derive analytic expressions of the Wigner functions, with negativity indicating nonclassicality. This work reveals that circular superpositions of squeezed states possess enhanced quantum features, which are relevant to quantum metrology and information processing.

DOI
10.1002/qute.70345

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ABSTRACT Inspired by the superposition of coherent states, we investigate the superposition of squeezed states (pure Gaussian states) and propose a mathematical characterization under the Fock‐Bargmann representation, with the possibility to further generalize to the superposition of non‐Gaussian states. We introduce generalized circular states constructed by superposing squeezed coherent states symmetrically on a circle. We demonstrate their photon distributions as “trimmed and rescaled” versions of those of the initial squeezed states. We find that squeezing disappears while higher‐order squeezing might be strengthened for some specific generalized circular states. We derive analytic expressions of the Wigner functions, with negativity indicating nonclassicality. This work reveals that circular superpositions of squeezed states possess enhanced quantum features, which are relevant to quantum metrology and information processing.
We show that superpositions of oppositely squeezed states -- non-Gaussian Schr{ö}dinger-cat-like states -- exhibit enhanced nonclassical features and provide an entanglement advantage in the small-squeezing regime. These states possess photon-number structures distinct from conventional coherent-state cat states, and we analyze their Wigner functions and the entanglement generated when they are injected into a 50-50 beam splitter. As a practical application, we demonstrate that they enable a high-quality heralded single-photon source whose second-order intensity correlation function is smaller than that obtained from a pure two-mode squeezed vacuum state. We further propose a linear-optical heralding scheme that approximates these superpositions without requiring strong Kerr nonlinearities. Our results indicate that the superposition of oppositely squeezed states is a promising non-Gaussian resource for quantum information processing, particularly for single-photon generation.
Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.
We define and study the properties of ``squeezed quantum multiplets''. Ordinary multiplets are sets of DDD-orthonormal quantum states formed by superpositions of states squeezed along DDD equally spaced directions in quadrature space. More generally, we also discuss superpositions of ``higher-order squeezed states'', including tri-squeezed and quad-squeezed states. All these states involve superpositions of multiples of ppp photons. We compare states in ordinary (p=2p=2p=2) multiplets and higher-order ones (p>2p>2p>2) in the most relevant cases, showing that ordinary squeezed multiplets and higher-order ones share some important similarities, as well as some differences. Finally, we present analytical expressions for phase-space distributions (Wigner and characteristic functions) representing ordinary squeezed multiplets. We use this to show that some squeezed multiplets are highly sensitive to perturbations in all phase-space directions, making them interesting for metrological applications.
ABSTRACT In this paper, we study new non‐Gaussian states known as superpositions of photon‐added and photon‐subtracted displaced Fock states (SPA‐PS‐DFSs). We express the SPA‐PS‐DFSs in terms of displaced Fock states (DFSs) and investigate their Wigner function and nonclassical properties. The obtained results of the Wigner function show that the superposition of photon addition and subtraction can enhance the non‐Gaussian and nonclassical properties of the SPA‐PS‐DFSs. Furthermore, the SPA‐PS‐DFSs exhibit nonclassical features, including higher‐order squeezing and higher‐order antibunching. Notably, these nonclassical characteristics are more enhanced than those of previous states generated solely by adding or subtracting photons to DFSs without superposition. These findings underscore the effectiveness of the superposition technique in enhancing the non‐Gaussian and nonclassical properties of the states.
With a squeezing operation on the qubit state,we obtain a coherent superposition state of a squeezed vacuum state and a squeezed single photon state with certain weight rate.The coherent superposition state depends on the squeezing parameter and weight factor,I and its nonclassicality and non-Gaussian properties are researched.It is investigated by the sub-Poissonian statistics distribution of Mandel′s Q parameter and the negativity of the Wigner function.The non-Gaussianity of coherent superposition qubit state can be improved by adjusting the squeezing parameter and the weight factor.