Non-Gaussian Quantum States and Where to Find Them
- URL: http://arxiv.org/abs/2104.12596v3
- Date: Tue, 27 Jul 2021 13:14:49 GMT
- Title: Non-Gaussian Quantum States and Where to Find Them
- Authors: Mattia Walschaers
- Abstract summary: We show how non-Gaussian states can be created by performing measurements on a subset of modes in a Gaussian state.
We demonstrate that Wigner negativity is a requirement to violate Bell inequalities and to achieve a quantum computational advantage.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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