Inductive Entanglement Classification of Four Qubits under SLOCC

Abstract

Using an inductive approach to classify multipartite entangled states under stochastic local operations and classical communication introduced recently by the authors [Phys. Rev. A 74, 052336 (2006)], we give the complete classification of four-qubit entangled pure states. Apart from the expected degenerate classes, we show that there exist eight inequivalent ways to entangle four qubits. In this respect, permutation symmetry is taken into account and states with a structure differing only by parameters inside a continuous set are considered to belong to the same class.

11 pages and no figures. Accepted in PRA

References in corpus (5)

• Three qubits can be entangled in two inequivalent ways
• Four qubits can be entangled in nine different ways
• Quantum inseparability as local pseudomixture
• Inductive classification of multipartite entanglement under SLOCC
• Classification of Tripartite Entanglement with one Qubit

Cited by in corpus (82)

• Experimental realization of Dicke states of up to six qubits for multiparty quantum networking
• Quantifying entanglement resources
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• SLOCC classification of n qubits invoking the proportional relationships for spectrums and for standard Jordan normal forms
• Four-qubit entanglement from string theory
• Generation of Symmetric Dicke States of Remote Qubits with Linear Optics
• The black-hole/qubit correspondence: an up-to-date review
• Entanglement Equivalence of $N$-qubit Symmetric States
• Majorana representation of symmetric multiqubit states
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Operational determination of multi-qubit entanglement classes via tuning of local operations
• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• On the Black-Hole/Qubit Correspondence
• Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing
• Digital-analog quantum simulation of generalized Dicke models with superconducting circuits
• The algebra of entanglement and the geometry of composition
• SLOCC invariant and semi-invariants for SLOCC classification of four-qubits
• Verifying multi-partite mode entanglement of W states
• Classification of Entanglement in Symmetric States
• Multi-qubit entanglement engineering via projective measurements
• Greenberger-Horne-Zeilinger generation protocol for N superconducting transmon qubits capacitively coupled to a quantum bus
• Entanglement structures in qubit systems
• Decoherence-free preparation of Dicke states of trapped ions by collective stimulated Raman adiabatic passage
• The invariant-comb approach and its relation to the balancedness of multipartite entangled states
• Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
• Entanglement of four qubit systems: a geometric atlas with polynomial compass I (the finite world)
• Characterizing multipartite symmetric Dicke states under the effects of noise
• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Geometric descriptions of entangled states by auxiliaries varieties
• Entanglement in highly symmetric multipartite quantum states
• Deterministic generation of arbitrary symmetric states and entanglement classes
• Classification of four-qubit entangled states via Machine Learning
• Entangled graphs: A classification of four-qubit entanglement
• Of Local Operations and Physical Wires
• Operational multipartite entanglement classes for symmetric photonic qubit states
• Production of multipartite entanglement for electron spins in quantum dots
• Understanding entanglement sudden death through multipartite entanglement and quantum correlations
• Entanglement and magnetic order
• Four-qubit pure states as fermionic states
• Operational Entanglement Families of Symmetric Mixed N-Qubit States
• Entanglement classification with matrix product states
• Entanglement of four-qubit systems: a geometric atlas with polynomial compass II (the tame world)
• Invariant-based entanglement monotones as expectation values and their experimental detection
• An algebraic classification of entangled states
• Classification scheme of pure multipartite states based on topological phases
• The compositional structure of multipartite quantum entanglement
• Classification of Multipartite Entanglement via Negativity Fonts
• Classifying Quantum Entanglement through Topological Links
• Entanglement Classification with Algebraic Geometry
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• State complexity and quantum computation
• The Parametric Symmetry and Numbers of the Entangled Class of 2 \times M \times N System
• Stochastic local operations and classical communication properties of the n-qubit symmetric Dicke states
• Decay of Entanglement for Solid-State Qubits
• Comment: Inductive entanglement classification of four qubits under stochastic local operation and classical communication
• Unitary Invariants and Classification of Four-Qubit States via Negativity Fonts
• Polynomial invariants of degree 4 for even-$n$ qubits and their applications in entanglement classification
• Classification of Bipartite and Tripartite Qutrit Entanglement under SLOCC
• Classification of the Entangled States of $2\times N\times N$
• The inductive entanglement classification yields ten rather than eight classes of four-qubit entangled states
• Reinforcement Learning Generation of 4-Qubits Entangled States
• A full dichotomy for Holant${}^c$, inspired by quantum computation
• Classification of four qubit states and their stabilisers under SLOCC operations
• The Necessary and Sufficient Conditions of Separability for Multipartite Pure States
• Non-gaussian Entanglement Swapping between Three-Mode Spontaneous Parametric Down Conversion and Three Qubits
• New invariants for entangled states
• Criteria for reliable entanglement quantification with finite data
• Stochastic local operations and classical communication equations and classification of even $n$ qubits
• Graphical Classification of Entangled Qutrits
• Higher order singular value decomposition and the reduced density matrices of three qubits
• Optimal Local Transformations of Flip and Exchange Symmetric Entangled States
• Maximal tree size of few-qubit states
• Classifying Entanglement by Algebraic Geometry
• Entanglement Classification of Restricted Greenberger-Horne-Zeilinger Symmetric States in Four-Qubit System
• A type of localized quadripartite entanglement
• Tree-size complexity of multiqubit states
• A Complete Set of Local Invariants for a Family of Multipartite Mixed States
• Greenberger-Horne-Zeilinger Symmetry in Four Qubit System
• Special core tensors of multi-qubit states and the concurrency of three lines
• Entanglement classification via integer partitions
• Testing equivalence of pure quantum states and graph states under SLOCC
• Rank-based SLOCC classification for odd n qubits