Entanglement sharing: from qubits to Gaussian states

Abstract

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such 'monogamy constraints' have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In these proceedings we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

11 pages. Proceedings of the workshop "Entanglement in physical and information sciences", Centro Ennio de Giorgi, Pisa, December 2004. (v2) References updated, final version published in Int. J. Quant. Inf

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• Continuous variable quantum information: Gaussian states and beyond
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Monogamy inequality for distributed Gaussian entanglement
• Continuous variable entanglement sharing in non-inertial frames
• Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Enhanced tripartite interactions in spin-magnon-mechanical hybrid systems
• Monogamy of the Entanglement of Formation
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Strong monogamy inequalities for four qubits
• Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
• Generation of genuine tripartite entanglement for continuous variables in de Sitter space
• Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
• Conditions for monogamy of quantum correlations in multipartite systems
• Genuine tripartite entanglement of W state subject to Hawking effect of a Schwarzschild black hole
• Transfer of quantum states and stationary quantum correlations in a hybrid optomechanical network
• A Quantum Information Perspective on Many-Body Dispersive Forces
• Significant enhancement in refrigeration and entanglement in auxiliary-cavity-assisted optomechanical systems