Witnessing genuine multipartite entanglement with positive maps

Abstract

We derive a general framework that connects every positive map with a corresponding witness for partial separability in multipartite quantum systems. We show that many previous approaches were intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by non-decomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.

4 pages, 1 figure, this time the correct file and some last minute comments included

References in corpus (26)

• Quantum entanglement
• Separability of Mixed States: Necessary and Sufficient Conditions
• Concentrating Partial Entanglement by Local Operations
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Entanglement detection
• 14-qubit entanglement: creation and coherence
• Unextendible Product Bases and Bound Entanglement
• Classification of mixed three-qubit states
• Inseparability criteria for bipartite quantum states
• Generation and Confirmation of a (100x100)-dimensional entangled Quantum System
• Taming multiparticle entanglement
• Separability criteria for genuine multiparticle entanglement
• Detection of high-dimensional genuine multi-partite entanglement of mixed states
• Device-independent entanglement quantification and related applications
• Optimal entanglement criterion for mixed quantum states
• Multipartite Entanglement Witnesses
• Entanglement and permutational symmetry
• The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
• Determining lower bounds on a measure of multipartite entanglement from few local observables
• Inequalities for the Ranks of Quantum States
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• Four-qubit entangled symmetric states with positive partial transpositions
• Conditions for entanglement in multipartite systems
• Entangled symmetric states of N qubits with all positive partial transpositions
• Separability criteria and entanglement witnesses for symmetric quantum states
• A unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities

Cited by in corpus (50)

• Entanglement Certification $-$ From Theory to Experiment
• Entanglement witnesses: construction, analysis and classification
• Relaxations of separability in multipartite systems: Semidefinite programs, witnesses and volumes
• Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation
• Semidefinite programming relaxations for quantum correlations
• Characterizing Genuine Multilevel Entanglement
• Genuine-multipartite entanglement criteria based on positive maps
• Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
• From unextendible product bases to genuinely entangled subspaces
• Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures
• Measure and detection of genuine multipartite entanglement for tripartite systems
• Genuine multipartite entanglement detection and lower bound of multipartite concurrence
• Construction of multi-qubit optimal genuine entanglement witnesses
• Detecting genuine multipartite entanglement via machine learning
• Positive maps and trace polynomials from the symmetric group
• Positive tensor products of qubit maps and n-tensor-stable positive qubit maps
• Entanglement properties of quantum grid states
• Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement
• Practical Entanglement Estimation for Spin-System Quantum Simulators
• Separability criteria via some classes of measurements
• Construction of genuine multipartite entangled states
• Resource conversion between operational coherence and multipartite entanglement in many-body systems
• Quantum Fisher information-based detection of genuine tripartite entanglement
• Measurement-based local quantum filters and their ability to transform quantum entanglement
• A generic framework for genuine multipartite entanglement detection
• A Hierarchy of Multipartite Correlations Based on Concentratable Entanglement
• Detection of Genuine Multipartite Entanglement in Multipartite Systems
• Detecting genuine multipartite entanglement in three-qubit systems with eternal non-Markovianity
• Necessary conditions for classifying m-separability of multipartite entanglements
• Detection of genuine tripartite entanglement based on Bloch representation of densitymatrices
• Genuine entanglement detection via projection map in multipartite systems
• Tripartite genuinely entangled states from entanglement-breaking subspaces
• Detection of multipartite entanglement based on Heisenberg-Weyl representation of density matrices
• Witness based nonlinear detection of quantum entanglement
• "All-versus-nothing" proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario
• Detecting genuine multipartite entanglement using moments of positive maps
• Interconversion between block coherence and multipartite entanglement in many-body systems
• Unified approach to geometric and positive-map-based non-linear entanglement identifiers
• Analysing multiparticle quantum states
• Detection of Genuine Multipartite Entanglement in Arbitrary Multipartite systems
• The Role of Localizable Concurrence in Quantum Teleportation Protocols
• Uniform Entanglement Frames
• A variational quantum algorithm for entanglement quantification
• Detection and measure of genuine tripartite entanglement with partial transposition and realignment of density matrices
• Characterizing multipartite entanglement by violation of CHSH inequalities
• Threetangle in the XY-model class with a non-integrable field background
• On Sufficient and Necessary Criteria of Multipartite Quantum Entanglement
• $4\times 4$ unextendible product basis and genuinely entangled space
• Conditions for 3-partite and 4-partite genuine entanglement
• Quantum Separability Criteria Based on Symmetric Measurements