Arboreal Bound Entanglement

Abstract

In this paper, we discuss the entanglement properties of graph-diagonal states, with particular emphasis on calculating the threshold for the transition between the presence and absence of entanglement (i.e. the separability point). Special consideration is made of the thermal states of trees, including the linear cluster state. We characterise the type of entanglement present, and describe the optimal entanglement witnesses and their implementation on a quantum computer, up to an additive approximation. In the case of general graphs, we invoke a relation with the partition function of the classical Ising model, thereby intimating a connection to computational complexity theoretic tasks. Finally, we show that the entanglement is robust to some classes of local perturbations.

9 pages + appendices, 3 figures

References in corpus (23)

• Entanglement detection
• Multi-party entanglement in graph states
• Optimization of entanglement witnesses
• Witnessing multipartite entanglement
• Quantum error-correcting codes associated with graphs
• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Separability criteria for genuine multiparticle entanglement
• Classification of multi-qubit mixed states: separability and distillability properties
• Entanglement Detection in the Stabilizer Formalism
• Multiparticle entanglement purification for graph states
• Multiparticle entanglement purification for two-colorable graph states
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Detecting multipartite entanglement
• State Transfer and Spin Measurement
• Quantitative verification of entanglement and fidelities from incomplete measurement data
• On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants
• Optimal purification of thermal graph states
• How long can a quantum memory withstand depolarizing noise?
• Macroscopic bound entanglement in thermal graph states
• Multipartite purification protocols: upper and optimal bounds
• A Witness of Multipartite Entanglement Strata
• Entanglement in pure and thermal cluster states
• Weight of quadratic forms and graph states

Cited by in corpus (10)

• Using Separable Bell-Diagonal States to Distribute Entanglement
• Optimal Detection of Entanglement in GHZ States
• Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits
• The Degree of Quantum Correlation Required to Speed-Up a Computation
• Estimating localizable entanglement from witnesses
• Distillation of free entanglement from bound entangled states using weak measurements
• Linear-optical simulation of the cooling of a cluster-state Hamiltonian system
• Genuine Entanglement of Four Qubit Cluster Diagonal States
• Characterizing generalized axisymmetric quantum states in $d\times d$ systems
• Nonlinear entanglement witnesses for four qubits in mutually unbiased bases