Entanglement and local information access for graph states

Abstract

We exactly evaluate a number of multipartite entanglement measures for a class of graph states, including d-dimensional cluster states (d = 1,2,3), the Greenberger-Horne-Zeilinger states, and some related mixed states. The entanglement measures that we consider are continuous, `distance from separable states' measures, including the relative entropy, the so-called geometric measure, and robustness of entanglement. We also show that for our class of graph states these entanglement values give an operational interpretation as the maximal number of graph states distinguishable by local operations and classical communication (LOCC), as well as supplying a tight bound on the fixed letter classical capacity under LOCC decoding.

8 pages, 4 figures, to appear in the special issue of New J. Phys. on measurement-based quantum information processing

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Cited by in corpus (48)

• Entanglement detection
• Quantum Resource Theories
• The geometric measure of entanglement for symmetric states
• Multiparticle entanglement under the influence of decoherence
• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Quantum phase transition between cluster and antiferromagnetic states
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• A resource theory of entanglement with a unique multipartite maximally entangled state
• Topological order in 1D Cluster state protected by symmetry
• Scalable Bell inequalities for qubit graph states and robust self-testing
• The geometric measure of entanglement for a symmetric pure state with positive amplitudes
• Phase transition of computational power in the resource states for one-way quantum computation
• Lower bounds on entanglement measures from incomplete information
• Additivity and non-additivity of multipartite entanglement measures
• Relative entropy of entanglement for certain multipartite mixed states
• Optimal verification of stabilizer states
• Classification of Entanglement in Symmetric States
• A comparison of old and new definitions of the geometric measure of entanglement
• Survival of entanglement in thermal states
• Universal resources for approximate and stochastic measurement-based quantum computation
• Generating topological order from a 2D cluster state using a duality mapping
• Entanglement of genuinely entangled subspaces and states: exact, approximate, and numerical results
• Direct evaluation of pure graph state entanglement
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• Entanglement under the renormalization-group transformations on quantum states and in quantum phase transitions
• Entanglement of graph states up to 8 qubits
• Efficient Entanglement Measure for Graph States
• Entanglement in pure and thermal cluster states
• Sharp complexity phase transitions generated by entanglement
• How much of one-way computation is just thermodynamics?
• Simple sufficient condition for subspace to be completely or genuinely entangled
• Highly-efficient estimation of entanglement measures for large experimentally created graph states via simple measurements
• Symmetric hypergraph states: Entanglement quantification and robust Bell nonlocality
• Optimal verification of entanglement in a photonic cluster state experiment
• Coherence and entanglement in Grover and Harrow-Hassidim-Lloyd algorithm
• An Extention of Entanglement Measures for Pure States
• Fidelity between a bipartite state and another one undergoing local unitary dynamics
• Multipartite entanglement and quantum error identification in $D$-dimensional cluster states
• Controlled remote implementation of operations via graph states
• Quantifying entanglement from the geometric perspective
• Many-body quantum resources of graph states
• Discrimination strategies for inequivalent classes of multipartite entangled states
• Identifying non-k-separability of a class of N-qubit complete graph states using correlation tensors
• Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner
• Entanglement bound for multipartite pure states based on local measurements
• Entanglement of stabilizer codewords
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement