Separability properties of tripartite states with UxUxU-symmetry

Abstract

We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension d. These are the states, which can be written as linear combinations of permutation operators, or, equivalently, commute with unitaries of the form UxUxU. We compute explicitly the following subsets and their extreme points: (1) triseparable states, which are convex combinations of triple tensor products, (2) biseparable states, which are separable for a twofold partition of the system, and (3) states with positive partial transpose with respect to such a partition. Tripartite entanglement is investigated in terms of the relative entropy of tripartite entanglement and of the trace norm.

16 pages, RevTeX, 14 figures. Extends quant-ph/0003008 with additional results. Submitted to Phys.Rev.A

References in corpus (3)

• Conditions for a class of entanglement transformations
• Unextendible Product Bases and Bound Entanglement
• Separability and distillability of multiparticle quantum systems

Cited by in corpus (92)

• Quantum entanglement
• Entanglement detection
• Classification of mixed three-qubit states
• Quantum Data Hiding
• Fundamentals of Quantum Information Theory
• Quantifying Entanglement with Witness Operators
• Optimal spin squeezing inequalities detect bound entanglement in spin models
• Spin squeezing and entanglement
• A classification of entanglement in three-qubit systems
• One-and-a-half quantum de Finetti theorems
• Quantifying entanglement resources
• Hiding classical data in multi-partite quantum states
• Genuine quantum correlations in quantum many-body systems: a review of recent progress
• Entanglement and permutational symmetry
• Permutationally invariant state reconstruction
• Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states
• Partial separability and entanglement criteria for multiqubit quantum states
• Classical Shadows With Noise
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Local Hidden Variable Theories for Quantum States
• Local hidden--variable models for entangled quantum states
• Entanglement criteria for Dicke states
• Analytical characterization of the genuine multiparticle negativity
• Robustness of incompatibility for quantum devices
• Genuine three-partite entangled states with a local hidden variable model
• QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB
• Consensus for Quantum Networks: From Symmetry to Gossip Iterations
• Quantum entanglement analysis based on abstract interpretation
• Entangled symmetric states of N qubits with all positive partial transpositions
• Canonical Decompositions of n-qubit Quantum Computations and Concurrence
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
• Orthogonality And Distinguishability: Criterion For Local Distinguishability of Arbitrary Orthogonal States
• Robust asymptotic entanglement under multipartite collective dephasing
• Unitary-invariant witnesses of quantum imaginarity
• A complete hierarchy for the pure state marginal problem in quantum mechanics
• Composite parameterization and Haar measure for all unitary and special unitary groups
• Efficient algorithm for multi-qudit twirling for ensemble quantum computation
• Measurement of Identical Particle Entanglement and the Influence of Antisymmetrisation
• Analysing quantum systems with randomised measurements
• Long-range multipartite entanglement close to a first order quantum phase transition
• Finding a maximally correlated state - Simultaneous Schmidt decomposition of bipartite pure states
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Compatible quantum correlations: on extension problems for Werner and isotropic states
• On multipartite invariant states I. Unitary symmetry
• Multipartite reduction criteria for separability
• Computing complexity measures for quantum states based on exponential families
• Efficient multi port-based teleportation schemes
• Optimization over trace polynomials
• Structure and properties of the algebra of partially transposed permutation operators
• Dimension-free entanglement detection in multipartite Werner states
• SLOCC Convertibility between Two-Qubit States
• Genuine tripartite entanglement in the non-interacting Fermi gas
• Collective randomized measurements in quantum information processing
• Programmability of covariant quantum channels
• Simple test for quantum channel capacity
• Positive maps and trace polynomials from the symmetric group
• Group representation approach to 1 - N universal quantum cloning machines
• Entangled symmetric states and copositive matrices
• A class of symmetric Bell diagonal entanglement witnesses - a geometric perspective
• Bounding the forward classical capacity of bipartite quantum channels
• Generating and protecting correlated quantum states under collective dephasing
• On multipartite invariant states II. Orthogonal symmetry
• Entanglement transitivity problems
• A priori probability that a qubit-qutrit pair is separable
• A Hierarchy of Multipartite Correlations Based on Concentratable Entanglement
• Squaring parametrization of constrained and unconstrained sets of quantum states
• Rotationally invariant bipartite states and bound entanglement
• Symmetric construction of reference-frame-free qudits
• Explicit constructions of unitary transformations between equivalent irreducible representations
• Linear programming with unitary-equivariant constraints
• Entanglement classes of symmetric Werner states
• Metrological usefulness of entanglement and nonlinear Hamiltonians
• On state vs. channel quantum extension problems: exact results for UxUxU symmetry
• Multiparticle singlet states cannot be maximally entangled for the bipartitions
• Efficient quantum algorithms for testing symmetries of open quantum systems
• A geometrical description of the universal $1\to 2$ asymmetric quantum cloning region
• Recovery With Incomplete Knowledge: Fundamental Bounds on Real-Time Quantum Memories
• Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation
• Geometric Multiaxial Representation of N-qubit Mixed Symmetric Separable States
• Stability of Flip and Exchange Symmetric Entangled State Classes under Invertible Local Operations
• On the state space structure of tripartite quantum systems
• Correlations, Bell Inequality Violation & Quantum Entanglement
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• Positive maps from the walled Brauer algebra
• Symmetric coupling of four spin-1/2 systems
• Entanglement Distillation using the Exchange Interaction
• Process-optimized phase covariant quantum cloning
• Refuting spectral compatibility of quantum marginals
• Geometric measures of quantum nonlocality: characterization, quantification, and comparison by distances and operations
• Werner states from diagrams
• Iterative construction of ${\mathfrak{S}}_p\times {\mathfrak{S}}_p$ group-adapted irreducible matrix units for the walled Brauer algebra
• Hilbert-Schmidt Geometry of n-Level Jakobczyk-Siennicki Two-Dimensional Quantum Systems