Optimal purification of thermal graph states

Abstract

In this paper, a purification protocol is presented and its performance is proven to be optimal when applied to a particular subset of graph states that are subject to local Z-noise. Such mixed states can be produced by bringing a system into thermal equilibrium, when it is described by a Hamiltonian which has a particular graph state as its unique ground state. From this protocol, we derive the exact value of the critical temperature above which purification is impossible, as well as the related optimal purification rates. A possible simulation of graph Hamiltonians is proposed, which requires only bipartite interactions and local magnetic fields, enabling the tuning of the system temperature.

5 pages, 4 figures v2: published version

References in corpus (14)

• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Persistent entanglement in arrays of interacting particles
• Measurement-based quantum computation with cluster states
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms
• Stability of macroscopic entanglement under decoherence
• Classification of multi-qubit mixed states: separability and distillability properties
• Multi-Particle Entanglement Purification Protocols
• Multiparticle entanglement purification for graph states
• Long-range quantum entanglement in noisy cluster states
• Multiparticle entanglement purification for two-colorable graph states
• Quantum Anonymous Transmissions
• Graph State Preparation and Cluster Computation with Global Addressing of Optical Lattices
• Quantum computation in optical lattices via global laser addressing

Cited by in corpus (18)

• Quantum entanglement
• Entanglement purification and quantum error correction
• Open-System Dynamics of Entanglement
• A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
• Purification of genuine multipartite entanglement
• Optimal Detection of Entanglement in GHZ States
• Gapped Two-Body Hamiltonian for continuous-variable quantum computation
• Survival of entanglement in thermal states
• Single-qubit rotations in 2D optical lattices with multi-qubit addressing
• Macroscopic bound entanglement in thermal graph states
• A Witness of Multipartite Entanglement Strata
• Multipartite purification protocols: upper and optimal bounds
• Entanglement in pure and thermal cluster states
• Reducing Computational Complexity of Quantum Correlations
• Arboreal Bound Entanglement
• Linear-optical simulation of the cooling of a cluster-state Hamiltonian system
• Bounding Fault-Tolerant Thresholds for Purification and Quantum Computation
• A modular entanglement-based quantum computer architecture