Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states

Abstract

We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (upon availability of an initial two-mode squeezed state). We analyze in depth the properties of distributed entanglement and the origin of its sharing structure, showing that the promiscuity of entanglement sharing is a feature peculiar to symmetric Gaussian states that survives even in the presence of significant degrees of mixedness and decoherence. Next, we discuss the suitability of the considered tripartite entangled states to the implementation of quantum information and communication protocols with continuous variables. This will lead to a feasible experimental proposal to test the promiscuous sharing of continuous-variable tripartite entanglement, in terms of the optimal fidelity of teleportation networks with Gaussian resources. We finally focus on the application of three-mode states to symmetric and asymmetric telecloning, and single out the structural properties of the optimal Gaussian resources for the latter protocol in different settings. Our analysis aims to lay the basis for a practical quantum communication with continuous variables beyond the bipartite scenario.

33 pages, 10 figures (some low-res due to size constraints), IOP style; (v2) improved and reorganized, accepted for publication in New Journal of Physics

References in corpus (56)

• Experimental quantum teleportation
• A computable measure of entanglement
• Quantum information with continuous variables
• Three qubits can be entangled in two inequivalent ways
• Distributed Entanglement
• Peres-Horodecki separability criterion for continuous variable systems
• Inseparability criterion for continuous variable systems
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
• Teleportation of Quantum States
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Extremal entanglement and mixedness in continuous variable systems
• Quantum telecloning and multiparticle entanglement
• Multipartite entanglement for continuous variables: A quantum teleportation network
• Tripartite Quantum State Sharing
• Detecting genuine multipartite continuous-variable entanglement
• Entanglement versus Correlations in Spin Systems
• Bound entangled Gaussian states
• The Real Symplectic Groups in Quantum Mechanics and Optics
• Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables
• Multiphoton Quantum Optics and Quantum State Engineering
• Experimental verification of a fully inseparable tripartite continuous-variable state
• Localizable Entanglement
• High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables
• Gaussian measures of entanglement versus negativities: the ordering of two-mode Gaussian states
• Universal cloning of continuous quantum variables
• Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
• Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence
• No-cloning theorem and teleportation criteria for quantum continuous variables
• Separability Properties of Three-mode Gaussian States
• Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation
• Quantum benchmark for storage and transmission of coherent states
• Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
• Monogamy inequality for distributed Gaussian entanglement
• Optimal entanglement witnesses for continuous-variable systems
• The optimal cloning of quantum coherent states is non-Gaussian
• Three-mode entanglement by interlinked nonlinear interactions in optical ${\chi }^{(2)}$ media
• Unitarily localizable entanglement of Gaussian states
• Quantum Teleportation with Continuous Variables: a survey
• Mode-Wise Entanglement of Gaussian States
• Equivalence between Entanglement and the Optimal Fidelity of Continuous Variable Teleportation
• Optimal N-to-M Cloning of Quantum Coherent States
• Continuous variable entanglement and quantum state teleportation between optical and macroscopic vibrational modes through radiation pressure
• Optical implementation of continuous-variable quantum cloning machines
• Quantification and scaling of multipartite entanglement in continuous variable systems
• Demonstration of quantum telecloning of optical coherent states
• Bright tripartite entanglement in triply concurrent parametric oscillation
• Improving fidelity of continuous-variable teleportation via local operations
• Entanglement frustration for Gaussian states on symmetric graphs
• Multimode entanglement and telecloning in a noisy environment
• Generic Entanglement and Standard Form for N-mode Pure Gaussian States
• Entanglement sharing: from qubits to Gaussian states
• Conditioning two-party quantum teleportation within a three-party quantum channel
• A Quantum Teleportation Game
• Asymmetric quantum channel for quantum teleportation
• Entanglement convertibility for infinite dimensional pure bipartite states
• Entanglement bounds of tripartite squeezed thermal states

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• Continuous-Variable Telecloning with Phase-Conjugate Inputs
• Theory of genuine tripartite nonlocality of Gaussian states
• Multipartite Continuous Variable Solution for the Byzantine Agreement Problem
• Continuous Variable Solution for Byzantine Agreement
• Gaussian tripartite entanglement out of equilibrium
• Multimode advantage in continuous variable quantum battery
• Standard forms and entanglement engineering of multimode Gaussian states under local operations
• Robustness of entangled states that are positive under partial transposition
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication
• Quantum Dense Coding Network using Multimode Squeezed States of Light
• Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations
• Genuine multipartite nonlocality of permutationally invariant Gaussian states
• Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations
• Ancillary Gaussian modes activate the potential to witness non-Markovianity
• Nonclassical resource for continuous variable telecloning with non-Gaussian advantage
• Memory effects displayed in the evolution of continuous variable system