Conditions for a Class of Entanglement Transformations

1998/11/30 by Michael A. Nielsen, M. A. Nielsen · 1,059 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic number #Algorithm #Alice and Bob #Bipartite graph #Class (philosophy) #Computer science #Discrete mathematics #LOCC #Majorization #Mathematical analysis #Mathematics #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Squashed entanglement #State (computer science) #Theoretical physics #Transformation (genetics) #W state #quant-ph

paper · pdf · doi:10.1103/physrevlett.83.436

published in Physical Review Letters 83(2), 436-439 (American Physical Society) · 4 pages. Title and some nomenclature changed. Minor errors fixed

openalex publication_date 1999/07/12 · arxiv created 1999/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Suppose Alice and Bob jointly possess a pure state, |\ensuremathψ〉. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform |\ensuremathψ〉 into another joint state |\ensuremathφ〉. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we find that there exist essentially different types of entanglement for bipartite quantum systems.

Citations

• Average entropy of a subsystem
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Matrix Analysis

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