A de Finetti representation for finite symmetric quantum states

2004/10/27 by Robert Koenig, Robert König, Renato Renner · 9 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Invariant (physics) #Mathematical physics #Mathematics #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Representation (politics) #Representation theory of the symmetric group #State (computer science) #State space #Symmetric group #quant-ph

paper · pdf · doi:10.1063/1.2146188

published as J. Math. Phys. 46, 122108 (2005) · 22 pages, LaTeX

arxiv created 2004/10/27 · openalex publication_date 2005/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.

Citations

• Quantum cryptography: Public key distribution and coin tossing
• Quantum cryptography based on Bell’s theorem
• Symmetric informationally complete quantum measurements
• A Generic Security Proof for Quantum Key Distribution
• Probability Inequalities for Sums of Bounded Random Variables

Cited by

• New approaches to almost i.i.d. information theory
• One-and-a-Half Quantum de Finetti Theorems
• Finite de Finetti Theorem for Infinite-Dimensional Systems
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Optimal detection of entanglement in Greenberger-Horne-Zeilinger states
• Loss-tolerant quantum cryptography with imperfect sources
• Catalytic Coherence
• Approximating the set of separable states using the positive partial transpose test
• The Lie algebraic significance of symmetric informationally complete measurements
• SECURITY OF QUANTUM KEY DISTRIBUTION