Entanglement of Formation for Isotropic States

2000/05/16 by Barbara M. Terhal, K. G. H. Vollbrecht, Karl Gerd H. Vollbrecht · 254 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Convex hull #Density matrix #Dimension (graph theory) #Function (biology) #Geometry #Isotropy #Mathematical physics #Mathematics #Multipartite entanglement #Peres–Horodecki criterion #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Qubit #Qutrit #Regular polygon #Separable state #Squashed entanglement #W state #quant-ph

paper · pdf · doi:10.1103/physrevlett.85.2625

published in Physical Review Letters 85(12), 2625-2628 (American Physical Society) · 4 pages RevTex

arxiv created 2000/05/16 · openalex publication_date 2000/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Schmidt number for density matrices
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model

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