The Entanglement of Formation for Isotropic States

Abstract

We give an explicit expression for the entanglement of formation for isotropic density matrices in arbitrary dimensions in terms of the convex hull of a simple function. For two qutrit isotropic states we determine the convex hull and we have strong evidence for its exact form for arbitrary dimension. Unlike for two qubits, the entanglement of formation for two qutrits or more is found to be a nonanalytic function of the maximally entangled fraction in the regime where the density matrix is entangled.

4 pages RevTex

Cited by in corpus (153)

• Quantum entanglement
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entanglement Measures under Symmetry
• Measures and dynamics of entangled states
• The asymptotic entanglement cost of preparing a quantum state
• Further results on the cross norm criterion for separability
• Entanglement of formation for symmetric Gaussian states
• Measure of genuine multipartite entanglement with computable lower bounds
• Fundamentals of Quantum Information Theory
• Open-System Dynamics of Entanglement
• Quantifying Entanglement with Witness Operators
• I-concurrence and tangle for isotropic states
• Quantifying entanglement resources
• Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
• Group-Invariant Quantum Machine Learning
• Entanglement and permutational symmetry
• Genuinely Multipartite Concurrence of N-qubit X-matrices
• Entanglement of Formation of Bipartite Quantum States
• Entanglement cost of mixed states
• Measuring Coherence with Entanglement Concurrence
• The geometric measure of entanglement for symmetric states
• Multiparticle entanglement under the influence of decoherence
• Upper bound and shareability of quantum discord based on entropic uncertainty relations
• The asymptotic relative entropy of entanglement
• Separability criteria and bounds for entanglement measures
• Concurrence Vectors in Arbitrary Multipartite Quantum Systems
• Nonlocal advantage of quantum coherence in high-dimensional states
• Entanglement of formation for an arbitrary two-mode Gaussian state
• Typical entanglement of stabilizer states
• Roofs and Convexity
• Remarks on additivity of the Holevo channel capacity and of the entanglement of formation
• Separability and correlations in composite states based on entropy methods
• Entanglement within the Quantum Trajectory Description of Open Quantum Systems
• A lower bound of concurrence for multipartite quantum states
• Quantify entanglement by concurrence hierarchy
• Quantifying quantum discord and entanglement of formation via unified purifications
• Tomography is necessary for universal entanglement detection with single-copy observables
• Estimating entanglement monotones with a generalization of the Wootters formula
• Useful states and entanglement distillation
• Local-dephasing-induced entanglement sudden death in two-component finite-dimensional systems
• Improved Semidefinite Programming Upper Bound on Distillable Entanglement
• Lower bounds on entanglement measures from incomplete information
• Linking Entanglement Detection and State Tomography via Quantum 2-Designs
• Highly Entangled Ground States in Tripartite Qubit Systems
• Entanglement of Formation for a Class of Quantum States
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
• Entanglement Rényi $\alpha$-entropy
• An Introduction to Quantum Entanglement: a Geometric Approach
• Bipartite entanglement of quantum states in a pair basis
• A Note on Fully Entangled Fraction
• Finite-time destruction of entanglement and non-locality by environmental influences
• Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures
• An Experimentally accessible geometric measure for entanglement in $N$-qubit pure states
• Efficient algorithm for multi-qudit twirling for ensemble quantum computation
• A Note on Entanglement of Formation and Generalized Concurrence
• Analytic Expressions for Geometric Measure of Three Qubit States
• A comparison of old and new definitions of the geometric measure of entanglement
• Pearson Correlation Coefficient as a measure for Certifying and Quantifying High Dimensional Entanglement
• A new parameterized entanglement monotone
• Experimental Determination of Entanglement for Arbitrary Pure States
• Entanglement for a two-parameter class of states in $2\otimes n$ quantum system
• Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
• Nonadditivity of Rains' bound for distillable entanglement
• Concurrence-based entanglement measure for Werner States
• Detecting and estimating continuous-variable entanglement by local orthogonal observables
• Magic-induced computational separation in entanglement theory
• Resilience of multi-photon entanglement under losses
• Evaluating the geometric measure of multiparticle entanglement
• A Class of Special Matrices and Quantum Entanglement
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• Duality and the geometric measure of entanglement of general multiqubit W states
• Quantifying entanglement of maximal dimension in bipartite mixed states
• Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states
• Designing Quantum Information Processing via Structural Physical Approximation
• Cloning quantum entanglement in arbitrary dimensions
• Sequential sharing of two-qudit entanglement based on the entropic uncertainty relation
• Quantum correlation exists in any non-product state
• Estimating multipartite entanglement measures
• On the irreversibility of entanglement distillation
• R Function Related to Entanglement of Formation
• Entanglement of formation for a class of $(2\otimes d)$-dimensional systems
• Lower Bound of Concurrence Based on Positive Maps
• Squeezing and entanglement in continous variable systems
• Discrete Fourier-based Correlations for Entanglement Detection
• Parameterized Bipartite Entanglement Measure
• Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory
• Improved lower and upper bounds for entanglement of formation
• Bounds of concurrence and their relation with fidelity and frontier states
• Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators
• Quantum Process Estimation via Generic Two-Body Correlations
• Many body physics from a quantum information perspective
• Average concurrence and entanglement swapping
• Entangled symmetric states and copositive matrices
• Quantum correlation induced by the average distance between the reduced states
• The ordering of energy levels for SU(n) symmetric antiferromagnetic chains
• Entanglement of Multipartite Schmidt-correlated States
• Quantifying mixed-state quantum entanglement by optimal entanglement witness
• Constrained bounds on measures of entanglement
• On 1-qubit channels
• Stable and metastable freezing of classical correlations in qutrits
• libCreme: An optimization library for evaluating convex-roof entanglement measures
• Evaluation of entanglement measures by a single observable
• Entanglement monotones and transformations of symmetric bipartite states
• Interference Visibility as a Witness of Entanglement and Quantum Correlation
• Entanglement Property and Monogamy Relation of Gerneralized Mixed W
• Quantum Coherence Versus Non-Classical Correlations in Optomechanics
• An analog of topological entanglement entropy for mixed states
• Lower bounds of concurrence for $N$-qubit systems and the detection of $k$-nonseparability of multipartite quantum systems
• Robust entangled states
• Complementarity and Entanglement in Quantum Information Theory
• Triangle inequalities in coherence measures and entanglement concurrence
• Lower and upper bounds for entanglement of Rényi-$\alpha$ entropy
• Estimating Parameterized Entanglement Measure
• A new bound of concurrence
• Estimating Concurrence via Entanglement Witnesses
• Additivity of entanglement of formation via entanglement-breaking space
• Method for measuring the entanglement of formation for arbitrary-dimensional pure states
• Bounds for multipartite concurrence
• Concurrence and Entanglement Entropy of Stochastic 1-Qubit Maps
• Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems
• Polynomial measure of coherence
• On the Activation of Quantum Nonlocality
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation
• A measure of quantum correlations that lies approximately between entanglement and discord
• A Note on Quantum Entanglement and PPT
• Finite-temperature Rydberg arrays: quantum phases and entanglement characterization
• Quantitative entanglement witnesses of Isotropic- and Werner-class via local measurements
• Frozen condition of quantum coherence
• A new entanglement measure based on the total concurrence
• Entanglement detection and lower bound of convex-roof extension of negativity
• Tripartite genuinely entangled states from entanglement-breaking subspaces
• General Depolarized Pure States: Identification and Properties
• Quantum Entanglement and Geometry
• Deterministic Twirling with Low Resources
• Does connected wedge imply distillable entanglement?
• Lower bound of multipartite concurrence based on sub-multipartite quantum systems
• Broken Symmetries in the Entanglement of Formation
• Differential Geometry of Bipartite Quantum States
• A total measure of multi-particle quantum correlations in atomic Schrödinger cat states
• Entanglement Generation and Dynamics for a Bose-Hubbard model in a Double-Well Potential
• Convex-roof entanglement measures of density matrices block diagonal in disjoint subspaces for the study of thermal states
• On the Fundamental Resource for Exponential Advantage in Quantum Channel Learning
• Analysis of the Entanglement Cost and Calculation of the Holevo Capacity
• Entanglement of formation for qubit-qudit system using partition of qudit sytem into a set of qubit system
• Some aspects of the interplay between bipartite correlations and quantum channels
• A resource theory of asynchronous quantum information processing
• End-to-end entanglement of quantum network paths with multi-parameter states
• Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
• Weak Schmidt decomposition and generalized Bell basis related to Hadamard matrices
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings