Non-Gaussian Quantum States and Where to Find Them (2104.12596v3)

Abstract: Gaussian states have played on 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 characterised 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 will 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 realisations of non-Gaussian quantum states in quantum optics and beyond.

• The paper presents frameworks to characterize non-Gaussian states using phase-space distributions and quantifies deviations from Gaussianity.
• It demonstrates that non-Gaussian states are essential for achieving quantum computational advantage and enhancing quantum correlations.
• Experimental techniques such as conditional preparation, advanced tomography, and improved detector technologies are detailed and evaluated.

Non-Gaussian Quantum States and Where to Find Them: An Overview

The paper "Non-Gaussian Quantum States and Where to Find Them" by Mattia Walschaers provides a comprehensive tutorial on the physics and characterization of non-Gaussian quantum states, primarily focusing on continuous-variable (CV) quantum systems. In contrast to Gaussian states, which are well understood and experimentally manageable due to their Gaussian nature in phase space, non-Gaussian states are less well-defined and present a multitude of challenges and opportunities for quantum technologies.

Key Contributions and Insights

The paper serves as a roadmap for understanding non-Gaussian quantum states in several aspects:

1. Characterization of Non-Gaussianity: The tutorial introduces various frameworks for characterizing non-Gaussian states, utilizing phase-space representations. It highlights the phase-space distributions like the Wigner function and discusses measures for non-Gaussianity, such as deviations from a Gaussian Wigner function by considering properties like stellar rank and quantum non-Gaussianity indicators.
2. Role in Quantum Technologies: Non-Gaussian states are identified as crucial for achieving quantum computational advantage, particularly in tasks like Boson Sampling, which are infeasible to efficiently simulate classically. The paper emphasizes the necessity of Wigner negativity as a resource for demonstrating quantum advantages in CV quantum computation.
3. Interplay with Quantum Correlations: The paper explores the relationship between non-Gaussian features and quantum correlations such as entanglement, steering, and Bell non-locality. Non-Gaussian operations can be used to enhance or even create quantum correlations, which are essential for various quantum information applications.
4. Conditional Preparation Techniques: The work details conditional preparation methods for creating non-Gaussian states. By performing specific measurements or applying certain operations, one can convert Gaussian states into non-Gaussian states, which can then be utilized for quantum experiments requiring strong non-classicality.
5. Experimental Realizations and Challenges: The tutorial reviews experimental advancements in producing non-Gaussian states in diverse settings like quantum optics, optomechanics, and superconducting circuits. It outlines the experimental hurdles and developments in tomography techniques and detector technologies essential for measuring and utilizing non-Gaussian states.

Implications and Future Directions

Theoretical and experimental advancements in non-Gaussian quantum states open several avenues for future research and application.

• Advancing Quantum Computation: By refining the understanding and control over non-Gaussian resources, CV quantum systems can be pushed towards more efficient and scalable quantum computational models, overcoming some of the limitations of purely Gaussian-based methods.
• Quantum Metrology and Communication: Non-Gaussian states could potentially offer enhancements in quantum metrology and secure quantum communication by exploiting their unique properties and entanglement capabilities.
• Expanding Experimental Capabilities: Continued development in photon-detection technologies, phase-space tomography, and the creation of sophisticated non-Gaussian states via conditional preparation will drive further experimental breakthroughs, supporting the theoretical findings with empirical evidence.

The paper underscores the essential role of non-Gaussian states in the broader quantum mechanics landscape, positioning them as vital components for next-generation quantum technologies, while also framing the challenges that lie ahead in harnessing their full potential.