Purification to Locally Maximally Entangleable States

Abstract

Locally maximally entangleable states (LMESs) constitute a large set of multipartite states, containing for instance all stabilizer states. LMESs are uniquely characterized by (2n-1) phases, where n denotes the number of qubits. We consider here those LMES whose phases are either 0 or π and present a multipartite entanglement purification protocol for arbitrary such states. In contrast to all previously known recurrence protocols this protocol uses a novel ingredient, which is required due to the quantum correlations contained in the various LMESs. We compare this scheme to previously known entanglement purification protocols and show that the direct purification performs better than previously known protocols.

References in corpus (19)

• Mixed State Entanglement and Quantum Error Correction
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Persistent entanglement in arrays of interacting particles
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Measurement-based quantum computation
• Multi-party entanglement in graph states
• Entanglement purification and quantum error correction
• Entangling operations and their implementation using a small amount of entanglement
• Multiparticle entanglement purification for graph states
• Multiparticle entanglement purification for two-colorable graph states
• Entanglement purification protocols for all graph states
• Multipartite Entanglement and Global Information
• Distillation of multipartite entanglement by complementary stabilizer measurements
• Entanglement Purification of Any Stabilizer State
• Purification of large bicolorable graph states
• A monomial matrix formalism to describe quantum many-body states
• Stabilizer state breeding
• Decoherence of many-body systems due to many-body interactions

Cited by in corpus (14)

• Open-System Dynamics of Entanglement
• Quantum Hypergraph States
• Multipartite entanglement measures
• Entanglement and nonclassical properties of hypergraph states
• Local unitary symmetries of hypergraph states
• Graph states and local unitary transformations beyond local Clifford operations
• Qudit Hypergraph States
• Remote entanglement preparation
• Diagonal-unitary 2-designs and their implementations by quantum circuits
• Entanglement Purification of Hypergraph States
• A modular entanglement-based quantum computer architecture
• Multipartite States under Elementary Local Operations
• Entanglement of $\pi$-LME states and the SAT problem
• Non-symmetric GHZ states: weighted hypergraph and controlled-unitary graph representations