A classification of entanglement in three-qubit systems

Abstract

We present a classification of three-qubit states based in their three-qubit and reduced two-qubit entanglements. For pure states these criteria can be easily implemented, and the different types can be related with sets of equivalence classes under Local Unitary operations. For mixed states characterization of full tripartite entanglement is not yet solved in general; some partial results will be presented here.

Shortened version. Accepted in EPJD

References in corpus (32)

• A computable measure of entanglement
• Three qubits can be entangled in two inequivalent ways
• Entanglement of a Pair of Quantum Bits
• Distributed Entanglement
• The logarithmic negativity: A full entanglement monotone that is not convex
• Separability criterion and inseparable mixed states with positive partial transposition
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Universal state inversion and concurrence in arbitrary dimensions
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entanglement monotones
• Classification of mixed three-qubit states
• Global entanglement in multiparticle systems
• Separability and distillability of multiparticle quantum systems
• Entangled three-qubit states without concurrence and three-tangle
• Multipartite generalisation of the Schmidt decomposition
• Three-qubit pure-state canonical forms
• Separability properties of tripartite states with UxUxU-symmetry
• Ordering two-qubit states with concurrence and negativity
• A comparative study of relative entropy of entanglement, concurrence and negativity
• Concurrence Vectors in Arbitrary Multipartite Quantum Systems
• Inductive classification of multipartite entanglement under SLOCC
• Multipartite entanglement in quantum spin chains
• Probability density function characterization of multipartite entanglement
• Entangled graphs: Bipartite entanglement in multi-qubit systems
• Concurrence in arbitrary dimensions
• Separability Criterion of Tripartite Qubit Systems
• Global Entanglement for Multipartite Quantum States
• Free Entanglement Measure
• Detection of N-particle entanglement with generalized Bell inequalities
• A simple entanglement measure for multipartite pure states
• Entangled graphs II: Classical correlations in multi-qubit entangled systems
• Existence Criterion of Genuine Tripartite Entanglement

Cited by in corpus (90)

• Efficient tomography of a quantum many-body system
• Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states
• Tri-partite Entanglement Witnesses and Sudden Death
• Generating Multimode Entangled Microwaves with a Superconducting Parametric Cavity
• Time-evolution of tripartite quantum discord and entanglement under local and non-local random telegraph noise
• Disentanglement, Bell-nonlocality violation and teleportation capacity of the decaying tripartite states
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Effect of Markov and Non-Markov Classical Noise on Entanglement Dynamics
• Quantum correlations and entanglement in a model comprised of a short chain of nonlinear oscillators
• Multipartite optomechanical entanglement from competing nonlinearities
• Entanglement Sudden Death in Three Qubit X-States
• Robust multipartite entanglement generation via a collision model
• Multipartite non-locality in a thermalized Ising spin-chain
• Entanglement swapping and swapped entanglement
• Quantum Correlations in non-Markovian Environments
• Maximum nonlocality in the (3,2,2) scenario
• Weaker entanglement guarantees stronger entanglement
• More nonlocality with less entanglement in a tripartite atom-optomechanical system
• Time-invariant entanglement and sudden death of nonlocality for multipartite systems under collective dephasing
• Protocols and quantum circuits for implementing entanglement concentration in cat state, GHZ-like state and 9 families of 4-qubit entangled states
• Photon exchange and correlations transfer in atom-atom entanglement dynamics
• Shareability of Quantum Steering and its Relation with Entanglement
• Information criteria for efficient quantum state estimation
• Complementary relations of entanglement, coherence, steering and Bell nonlocality inequality violation in three-qubit states
• Multipartite entanglement measures: a review
• The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels
• Tripartite thermal correlations in an inhomogeneous spin-star system
• Genuine Tripartite Entanglement in a Spin-Star Network at Thermal Equilibrium
• Tripartite entanglement transfer from flying modes to localized qubits
• Entangled graphs: A classification of four-qubit entanglement
• Analytical expression of Genuine Tripartite Quantum Discord for Symmetrical X-states
• A measure of tripartite entanglement in bosonic and fermionic systems
• Non equilibrium dissipation-driven steady many-body entanglement
• N-dimensional alternate coined quantum walks from a dispersion relation perspective
• Multiqubit entanglement and quantum phase gates with epsilon-near-zero plasmonic waveguides
• The role of entanglement for enhancing the efficiency of quantum kernels towards classification
• Tripartite entanglement in quantum memristors
• Generation and protection of Maximally Entangled State between many modes in an optical network with dissipation
• Generation of a time-bin Greenberger--Horne--Zeilinger state with an optical switch
• Dynamic generation of GHZ states with coupled charge qubits
• Multipartite entanglement transfer in spin chains
• Characterizing Entanglement Sources
• Entanglement generation between distant spins via quasilocal reservoir engineering
• Experimental linear-optics simulation of the ground state of an interacting quantum spin-ring
• Entanglement Sudden Death in a Quantum Memory
• Structural change in multipartite entanglement sharing: a random matrix approach
• Entanglement in a three spin system controlled by electric and magnetic field
• Robust quantum entanglement and teleportation in the tetrapartite spin-1/2 square clusters: Theoretical study on the effect of a cyclic four-spin exchange
• Molecular Nanomagnet ${\text{Cu}}^{\text{II}}{\text{Ni}}^{\text{II}}{\text{Cu}}^{\text{II}}$ as Resource for Bipartite and Tripartite Quantum Entanglement and Coherence
• Entanglement and quantum teleportation via decohered tripartite entangled states
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Quantifications for multi-mode entanglement
• Non-distillable entanglement guarantees distillable entanglement
• Influence of intrinsic decoherence on tripartite entanglement and bipartite fidelity of polar molecules in pendular states
• Deterministic transformations of three-qubit entangled pure states
• Quantum dissonance provide power to deterministic quantum computation with single qubit
• State mapping and discontinuous entanglement transfer in a multipartite open system
• Entanglement of one-magnon Schur-Weyl states
• A geometric formulation to measure global and genuine entanglement in three-qubit systems
• Vector Properties of Entanglement in a Three-Qubit System
• Quantum Information Aspects on Bulk and Nano Interacting Fermi System: Spin-Space Density Matrix Approach
• Tripartite quantum state mapping and discontinuous entanglement transfer in a cavity QED open system
• Anatomy of entanglement and nonclassicality criteria
• Experimental construction of a symmetric three-qubit entangled state and its utility in testing the violation of a Bell inequality on an NMR quantum simulator
• Classification witness operator for the classification of different subclasses of three-qubit GHZ class
• Mixture of entangled pure states with maximally mixed one-qudit reduced density matrices
• Experimental implementation of Hardy-like quantum pigeonhole paradoxes
• Multipartite Entanglement and Quantum Sensing in a Spin-5/2 Heisenberg Molecular Iron(III) Triangle
• Nonequilibrium steady states in multi-bath quantum collision models
• Light-pulse atom interferometry with entangled atom-optical elements
• Fate of multiparticle entanglement when one particle becomes classical
• Competition of Direct and Indirect Sources of Thermal Entanglement in a spin star network
• Storing Small Photonic Cluster States in a Dephasing Environment
• A Sharp Geometric Measure of Entanglement
• Three-Qubit State Preparation: Classification and Explicit Circuits
• The quantification of a genuine tetrapartite entanglement in a mixed spin-(1/2,1) Heisenberg tetramer
• W-class states-identification and quantification of Bell-CHSH inequalities' violation
• Optimal entanglement generation in GHZ-type states
• Manipulation of Multipartite Entanglement in an Array of Quantum Dots
• Entanglement of Assistance as a measure of multiparty entanglement
• Two- and three-mode squeezing in a three-qubit entangled system
• Dynamics of tripartite correlations for three qubits in independent thermal reservoirs
• Quantum Correlations in a Few-Atom Spin-1 Bose-Hubbard Model
• Tripartite entanglement in mixed-spin triangle trimmer
• Micromagnons and long-range entanglement in ferrimagnetic ground states
• Robust Tripartite Entanglement Generation via Correlated Noise in Spin Qubits
• Dynamics of multi-qubit systems in noisy environment
• Decoherence-free subspaces and Markovian revival of genuine multipartite entanglement in a dissipative system
• Evolution of tripartite entanglement in three-qubit Quantum Gravity-Induced Entanglement of Masses (QGEM) with quantum decoherence
• Tripartite Entanglement in Multimode Cavity Quantum Electrodynamics