Quantum optics in the phase space - A tutorial on Gaussian states

Abstract

In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In particular, we address their manipulation, evolution and characterization in view of their application to quantum information.

Tutorial. 23 pages, 1 figure. Updated version accepted for publication in EPJ - ST devoted to the memory of Federico Casagrande

References in corpus (19)

• Gaussian Quantum Information
• Quantum discord and the power of one qubit
• Experimental quantum computing without entanglement
• Quantum information can be negative
• No-local-broadcasting theorem for quantum correlations
• Symplectic invariants, entropic measures and correlations of Gaussian states
• Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
• Recent developments in photon-level operations on travelling light fields
• Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers
• Uhlmann fidelity between two-mode Gaussian states
• Full characterization of Gaussian bipartite entangled states by a single homodyne detector
• Entanglement and purity of two-mode Gaussian states in noisy channels
• Entanglement oscillations in non-Markovian quantum channels
• Quantum discord and local demons
• Mode-Wise Entanglement of Gaussian States
• Nonlinear quantum metrology using coupled nanomechanical resonators
• Entanglement of formation for an arbitrary two-mode Gaussian state
• A Condition for the Nullity of Quantum Discord
• Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals

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