Continuous Variable Quantum Information: Gaussian States and Beyond

By Gerardo Adesso, Sammy Ragy, Antony R. Lee. Open systems & information dynamics, 2014

615 citations recorded by the source corpus.

The study of Gaussian states has arisen to a privileged position in contin- uous variable quantum information in recent years. This is due to vehemently pursued experimental realisations and a magnificently elegant mathematical framework. In this paper, we provide a brief, and hopefully didactic, exposition of Gaussian state quantum information and its contemporary uses, including sometimes omitted crucial details. After introducing the subject material and outlining the essential toolbox of continuous variable systems, we define the basic notions needed to understand Gaussian states and Gaussian operations. In particular, emphasis is placed on the mathematical structure combining notions of algebra and symplectic geometry fundamental to a complete understanding of Gaussian informatics. Furthermore, we discuss the quantification of different forms of cor- relations (including entanglement and quantum discord) for Gaussian states, paying special attention to recently developed measures. The paper is concluded by succinctly expressing the main Gaussian state limitations and outlining a selection of possible future lines for quantum information processing with continuous variable systems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/491101c1cab945518612386841c7f52cd3d1d7c3

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Citations in the corpus

Complexity and entanglement for thermofield double states (2018, background): “that map Gaussian states into Gaussian states [80, 81].”
Advances in quantum cryptography (2019, neutral): “Quantum information [1–11] is the core science behind the so-called second quantum revolution [12, 13], or quantum 2.”
Quantum Fisher information matrix and multiparameter estimation (2019, neutral): “, [55, 56,58,60,61] χ(~s) = e− 1 2 ~sTΩCΩT~s−i(Ω〈~ R〉)T~s, (60) W (~ R) = 1 (2π)m √ detC e− 1 2( R−〈~ R〉) T C−1(~ R−〈~ R〉), (61)”
Entanglement certification from theory to experiment (2018, background): “These challenges already arise for finite-dimensional systems, which we focus on here, referring the interested reader to existing reviews on continuous-variable entanglement [30–35], for a discussion of the fascinating intricacies of infinite-dimensional systems.”
Continuous-variable quantum neural networks (2018, background): “Rather, it can be thought of as a type of digital quantum hardware [40], only partially suited to continuous-valued problems [41, 42].”
Modes and states in quantum optics (2019, background): “There are already a number of review papers and books that cover parts of this domain (Adesso and Illuminati, 2007a; Adesso et al., 2014; Ansari et al., 2018; Braunstein and Pati, 2012; Bruss and Leuchs, 2019; Furusawa, 2015; Grynberg et al., 2010; Leuchs and Korolkova, 2019; Ou, 2017; Simon et al.,”