Characterization of Gaussian operations and distillation of Gaussian states
Geza Giedke,J. Ignacio Cirac +1 more
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TLDR
It is shown that Gaussian states cannot be distilled by local Gaussian operations and classical communication, and positive (but not completely positive) Gaussian maps are defined.Abstract:
We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations that can be performed on Gaussian states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes that can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that Gaussian states cannot be distilled by local Gaussian operations and classical communication. We also define and characterize positive (but not completely positive) Gaussian maps.read more
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Continuous variable quantum information: Gaussian states and beyond
TL;DR: In this article, the authors provide a brief, and hopefully didactic, exposition of Gaussian state quantum information and its contemporary uses, including sometimes omitted crucial details, and discuss the quantification of different forms of entanglement and quantum discord for Gaussian states.
Journal ArticleDOI
Continuous variable quantum information: Gaussian states and beyond
TL;DR: The basic notions needed to understand Gaussian states and Gaussian operations are defined, and emphasis is placed on the mathematical structure combining notions of algebra and symplectic geometry fundamental to a complete understanding of Gaussian informatics.
Journal ArticleDOI
Entanglement, einstein-podolsky-rosen correlations, bell nonlocality, and steering
TL;DR: In this article, the authors defined steerable states, a type of quantum non-localality that is logically distinct from both nonseparability and Bell non-locality, and proved that steerable state are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality.
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Entanglement properties of the harmonic chain
TL;DR: In this article, the entanglement properties of a closed chain of harmonic oscillators coupled via a translationally invariant Hamiltonian were studied, where the coupling acts only on the position operators.
Journal ArticleDOI
Hybrid discrete- and continuous-variable quantum information
TL;DR: The traditional approaches to quantum information processing using either discrete or continuous variables can be combined in hybrid protocols for tasks including quantum teleportation, computation, entanglement distillation or Bell tests.
References
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Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Measuring the Quantum State of Light
TL;DR: In this paper, the authors present a method for simultaneous measurement of position and momentum in a simple optical instrument with respect to the quantum theory of light and quasiprobability distribution.
Book
Measuring the Quantum State of Light
TL;DR: In this paper, the authors present a method for simultaneous measurement of position and momentum in a simple optical instrument with respect to the quantum theory of light and quasiprobability distribution.
Journal ArticleDOI
Generalized Coherent States
TL;DR: In this paper, the generalized coherent states were studied using an operator technique similar to one we have used in a previous paper, and an alternative derivation of the most general coherent state was provided.