On multi-particle entanglement

Abstract

We build, using group-theoretic methods, a general framework for approaching multi-particle entanglement. As far as entanglement is concerned, two states of n spin-1/2 particles are equivalent if they are on the same orbit of the group of local rotations (U(2)^n). We give a method for finding the number of parameters needed to describe inequivalent n spin-1/2 particles states. We also describe how entanglement of states on a given orbit may be characterized by the stability group of the action of the group of local rotations on any point on the orbit.

16 pages, LaTeX

Cited by in corpus (86)

• Quantum entanglement
• Three qubits can be entangled in two inequivalent ways
• Distributed Entanglement
• Persistent entanglement in arrays of interacting particles
• Robustness of entanglement
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Global entanglement in multiparticle systems
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Classification of multi-qubit mixed states: separability and distillability properties
• Separability and distillability of multiparticle quantum systems
• Classification of multipartite entangled states by multidimensional determinants
• Multi-particle entanglement and its applications to cryptography
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps
• A Note on Invariants and Entanglements
• Multipartite generalisation of the Schmidt decomposition
• Three-qubit pure-state canonical forms
• The maximally entangled set of multipartite quantum states
• On local invariants of pure three-qubit states
• Purifying noisy entanglement requires collective measurements
• Local symmetry properties of pure 3-qubit states
• Black Holes, Qubits and Octonions
• On Multipartite Pure-State Entanglement
• The black-hole/qubit correspondence: an up-to-date review
• Activating bound entanglement in multi-particle systems
• Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition
• Freudenthal triple classification of three-qubit entanglement
• Nonlocal Properties and Local Invariants for Bipartite Systems
• On maximal entanglement between two pairs in four-qubit pure states
• Three-party entanglement from positronium
• Bipartite Mixed States of Infinite-Dimensional Systems are Generically Nonseparable
• Partial separability revisited: Necessary and sufficient criteria
• Parametrization and distillability of three-qubit entanglement
• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
• How many CNOT gates does it take to generate a three-qubit state ?
• Separability of Rank Two Quantum States
• Topological phases and multiqubit entanglement
• Properties of Entanglement Monotones for Three-Qubit Pure States
• Reversible combination of inequivalent kinds of multipartite entanglement
• Local Unitary Equivalence of Multi-qubit Mixed quantum States
• Separability and entanglement in 2x2xN composite quantum systems
• Range criterion and classification of true entanglement in $2\times M\times N$ system
• Complete set of operational measures for the characterization of 3-qubit entanglement
• Superqubits
• Classification of multipartite entanglement containing infinitely many kinds of states
• Criterion of Local Unitary Equivalence for Multipartite States
• Entanglement quantification through local observable correlations
• Classification and Quantification of Entangled Bipartite Qutrit Pure States
• Generalized Bloch Spheres for m-Qubit States
• Extremal Entanglement For Triqubit Pure States
• Geometric local invariants and pure three-qubit states
• Classification scheme of pure multipartite states based on topological phases
• Separability of rank two quantum states on multiple quantum spaces
• Topology of the three-qubit space of entanglement types
• Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group
• Deterministic LOCC transformation of three-qubit pure states and entanglement transfer
• Separability conditions based on local fine-grained uncertainty relations
• Unraveling the emergence of quantum state designs in systems with symmetry
• Classification of nonproduct states with maximum stabilizer dimension
• Maximum stabilizer dimension for nonproduct states
• All degree six local unitary invariants of k qudits
• Classification of the Entangled States of $2\times N\times N$
• Local unitary invariants for multipartite states
• On the units of bipartite entanglement: Is sixteen ounces of entanglement always equal to one pound?
• The stabilizer dimension of graph states
• Nilpotent polynomials approach to four-qubit entanglement
• Characterization of maximally entangled two-qubit states via the Bell-Clauser-Horne-Shimony-Holt inequality
• Local invariants of braiding quantum gates -- associated link polynomials and entangling power
• Introduction to quantum entanglement in many-body systems
• Entanglement and spin squeezing properties for three bosons in two modes
• Classification of n-qubit states with minimum orbit dimension
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• Using Partial Transpose and Realignment to generate Local Unitary Invariants
• Resource state structure for controlled quantum key distribution
• Sequential generation of Polynomial Invariants and N-body non-local correlations
• Invariant and polynomial identities for higher rank matrices
• Local unitary symmetries and entanglement invariants
• Local unitary equivalent consistence for n-party states and their (n-1)-party reduced density matrices
• On a suggestion relating topological and quantum mechanical entanglements
• Relation between three-qubit entanglement invariants and two-qubit concurrence
• Rényi and Tsallis formulations of separability conditions in finite dimensions
• Local Unitary Invariants for Multipartite Quantum Systems
• The average determinant of the reduced density matrices for each qubit as a global entanglement measure
• Low degree Lorentz invariant polynomials as potential entanglement invariants for multiple Dirac spinors
• Entanglement groups
• Lorentz invariants of pure three-qubit states