Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure

Abstract

We investigate the structural aspects of genuine multipartite entanglement in Gaussian states of continuous variable systems. Generalizing the results of [Adesso & Illuminati, Phys. Rev. Lett. 99, 150501 (2007)], we analyze whether the entanglement shared by blocks of modes distributes according to a strong monogamy law. This property, once established, allows to quantify genuine N-partite entanglement in terms of the "residual contangle" not encoded into 2,...,K,...,(N-1)-partite quantum correlations. The explicit expression of this entanglement measure is derived, by a recursive formula, for a subclass of Gaussian states. These are fully symmetric (permutation-invariant) states multi-partitioned into blocks, each consisting of an arbitrary number of modes. We compute the genuine multipartite entanglement shared by the blocks ("molecules") and investigate its scaling properties with the number and size of the molecules, the total number of modes, the global mixedness of the state, and the squeezed resources. To achieve the exact computation we prove a general result of symplectic analysis: Correlations among K molecules in N-mode multi-symmetric Gaussian states can be transformed by a local unitary operation into correlations shared by K single modes, one per molecule, in effective non-symmetric states. Due to this theorem, the above results extend to the subclass of non-symmetric Gaussian states that are obtained by unitarily localizing the multipartite molecular entanglement of symmetric states. These findings provide evidence that distributed Gaussian entanglement is strongly monogamous even beyond specific symmetry constraints, and that the residual contangle is a bona fide measure of genuine multipartite entanglement for permutation-invariant Gaussian states under any multi-partition of the modes.

arXiv comment19 pages, 7 figures; web and paper abstracts differ; published version

References in corpus (55)

• A computable measure of entanglement
• Quantum information with continuous variables
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Distributed Entanglement
• Peres-Horodecki separability criterion for continuous variable systems
• The logarithmic negativity: A full entanglement monotone that is not convex
• Entanglement in continuous variable systems: Recent advances and current perspectives
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entanglement monotones
• Extremal entanglement and mixedness in continuous variable systems
• Monogamy of entanglement and other correlations
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Multipartite entanglement for continuous variables: A quantum teleportation network
• Tripartite Quantum State Sharing
• Bound entangled Gaussian states
• "Squashed Entanglement" - An Additive Entanglement Measure
• Gaussian transformations and distillation of entangled Gaussian states
• Hudson's Theorem for finite-dimensional quantum systems
• An improved bound on distillable entanglement
• Symmetry implies independence
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Gaussian measures of entanglement versus negativities: the ordering of two-mode Gaussian states
• Is Entanglement Monogamous?
• 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
• A rigorous treatment of distillable entanglement
• Quantitative entanglement witnesses
• Gaussian Entanglement of Formation
• Estimating entanglement measures in experiments
• Studying quantum spin systems through entanglement estimators
• Monogamy inequality for distributed Gaussian entanglement
• Determination of continuous variable entanglement by purity measurements
• All entangled states are useful for information processing
• Violation of monogamy inequality for higher-dimensional objects
• Unitarily localizable entanglement of Gaussian states
• Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
• Hierarchies of Geometric Entanglement
• Mode-Wise Entanglement of Gaussian States
• Equivalence between Entanglement and the Optimal Fidelity of Continuous Variable Teleportation
• Quantification and scaling of multipartite entanglement in continuous variable systems
• An operational interpretation for multipartite entanglement
• Entanglement Monogamy of Tripartite Quantum States
• Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• GHZ extraction yield for multipartite stabilizer states
• Entanglement sharing: from qubits to Gaussian states
• Not-so-normal mode decomposition
• Multipartite Continuous Variable Solution for the Byzantine Agreement Problem
• Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
• Continuous Variable Solution for Byzantine Agreement
• Monogamy and ground-state entanglement in highly connected systems
• Correlated entanglement distillation and the structure of the set of undistillable states

Cited by in corpus (24)

• Quantum discord and its allies: a review
• Monogamy of quantum correlations - a review
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• General Monogamy of Tsallis $q$-Entropy Entanglement in Multiqubit Systems
• Gaussian entanglement revisited
• Optimal Distributed quantum sensing using Gaussian states
• Monogamy of quantum correlations in three qubit pure states using Rajagopal-Rendell (RR) quantum deficit
• Manipulating the quantum information of the radial modes of trapped ions: Linear phononics, entanglement generation, quantum state transmission and non-locality tests
• Gaussian tripartite steering in Schwarzschild black hole
• Conditions for monogamy of quantum correlations in multipartite systems
• Entanglement of two harmonic modes coupled by angular momentum
• Evaluation of ground state entanglement in spin systems with the random phase approximation
• A Common Parametrization for Finite Mode Gaussian States, their Symmetries and associated Contractions with some Applications
• Thermally induced entanglement of atomic oscillators
• Continuous variable multipartite vibrational entanglement
• Multimode theory of Gaussian states in uniformly accelerated frames
• Realization of the tradeoff between internal and external entanglement
• A Computable Criterion for Partial Entanglement in Continuous Variable Quantum Systems
• Even-odd entanglement in boson and spin systems
• Genuine multipartite nonlocality of permutationally invariant Gaussian states
• Entanglement and area laws in weakly correlated gaussian states
• Monogamous property of generalized W states in three-qubit systems in terms of relative entropy of entanglement
• Computable constraints on entanglement-sharing of multipartite quantum states
• Strain induced coupling and quantum information processing with hexagonal boron nitride quantum emitters