Multipartite pure-state entanglement

1998/11/30 by Ashish V. Thapliyal · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Bipartite graph #Discrete mathematics #Mathematical analysis #Mathematics #Multipartite #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 #Separable space #Separable state #Squashed entanglement #State (computer science) #W state #quant-ph

paper · pdf · doi:10.1103/physreva.59.3336

published as Phys.Rev. A59 (1999) 3336 · 8 Pages ReVTeX, 4 figures (eps); v2: Revised terminology, added two references and other minor changes; v3: Minor changes, added two references, added author's middle initial; v4: One footnote removed

arxiv created 1999/02/18 · openalex publication_date 1999/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that pure states of multipartite quantum systems are multiseparable (i.e., give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the quantification of multipartite pure-state entanglement are discussed. Further, as an application of the techniques used here, we show that any purification of a bipartite-bound entangled state having a positive partial transpose is tri-inseparable, i.e., has none of its three bipartite partial traces separable.

Citations

• Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Fidelity for Mixed Quantum States
• Higher order Schmidt decompositions
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Separability Criterion for Density Matrices
• Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
• Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels
• Die gegenw�rtige Situation in der Quantenmechanik
• Separability of mixed states: necessary and sufficient conditions
• Quantum theory, the Church–Turing principle and the universal quantum computer
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I
• Quantifying Entanglement
• A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II

Cited by

• Multipartite Entanglement for Continuous Variables: A Quantum Teleportation Network