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Physics-Uspekhi

On 'Schrödinger's cat' fringes

Valentin L. Gorshenin, Boulat N. Nougmanov, Farit Ya. Khalili

Published May 1, 2024• 1 citation
Publisher

Abstract

Non-Gaussian quantum states whose Wigner functions can take negative values are important both for fundamental tests of quantum physics and for the quantum information technologies that have been under active development recently.A typical example of a non-Gaussian state is the so-called Schr odinger's cat state.Its very interesting feature is that its `classical' part (two Gaussian maxima) is geometrically separated from the `nonclassical' part (interference fringes).In this paper, several methodological issues related to these fringes are considered.

DOI
10.3367/ufne.2024.05.039686

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Non-Gaussian quantum states whose Wigner functions can take negative values are important both for fundamental tests of quantum physics and for the quantum information technologies that have been under active development recently.A typical example of a non-Gaussian state is the so-called Schr odinger's cat state.Its very interesting feature is that its classical' part (two Gaussian maxima) is geometrically separated from the nonclassical' part (interference fringes).In this paper, several methodological issues related to these fringes are considered.
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In the present PhD work, we focus on a specific class of quantum states of light: the non-Gaussian states. These states have the particularity of exhibiting Wigner functions with some negative values. This quantum feature is a necessary condition to perform some quantum computation task; furthermore it is also useful for various other applications, including quantum communication and metrology. Different strategies can be used to generate these states. Here, we start from Gaussian states produced by optical parametric oscillators in the continuous wave regime, (i.e. single-mode and two-mode squeezed vacuum states). The non-Gaussian feature can only be obtained by non-linear phenomena (over-quadratic Hamiltonian). In our case, the non-linearity is induced by photon-counting-based measurements (also called non-Gaussian measurements). This study is mainly divided into two parts. First, the generation of non-classical states associated with two types of qubit encoding: the single-photon state, used for quantum information with discrete variables, and the coherent state superposition (the so-called optical Schrödinger cat state), used for quantum information with continuous variables. These two states have then been used to perform some quantum information protocols. The first one addresses the problem of single-photon entanglement witness, and the other the generation of entanglement between the two encodings (also called hybrid entanglement).
Highly quantum nonlinear interactions between different bosonic modes lead to the generation of quantum non-Gaussian states, i.e. states that cannot be written as mixtures of Gaussian states. A paradigmatic example is given by Schrödinger's cat states, that is, coherent superpositions of coherent states with opposite amplitude. We here consider a novel quantum non-Gaussianity criterion recently proposed in the literature and prove its effectiveness on Schrödinger cat states evolving in a lossy bosonic channel. We prove that the quantum non-Gaussianity can be effectively detected for high values of losses and for large coherent amplitudes of the cat states.
Gaussian states have played an important role in the physics of continuous-variable quantum systems.They are appealing for the experimental ease with which they can be produced, and for their compact and elegant mathematical description.Nevertheless, many proposed quantum technologies require us to go beyond the realm of Gaussian states and introduce non-Gaussian elements.In this Tutorial, we provide a roadmap for the physics of non-Gaussian quantum states.We introduce the phase-space representations as a framework to describe the different properties of quantum states in continuous-variable systems.We then use this framework in various ways to explore the structure of the state space.We explain how non-Gaussian states can be characterized not only through the negative values of their Wigner function, but also via other properties such as quantum non-Gaussianity and the related stellar rank.For multimode systems, we are naturally confronted with the question of how non-Gaussian properties behave with respect to quantum correlations.To answer this question, we first show how non-Gaussian states can be created by performing measurements on a subset of modes in a Gaussian state.Then, we highlight that these measured modes must be correlated via specific quantum correlations to the remainder of the system to create quantum non-Gaussian or Wigner-negative states.On the other hand, non-Gaussian operations are also shown to enhance or even create quantum correlations.Finally, we demonstrate that Wigner negativity is a requirement to violate Bell inequalities and to achieve a quantum computational advantage.At the end of the Tutorial, we also provide an overview of several experimental realizations of non-Gaussian quantum states in quantum optics and beyond.