2013/10/08 by Mathieu Lewin, Phan Thành Nam, Lewin, Mathieu +3
Computer Science · Mathematics · Physics and Astronomy · #Density matrix #FOS: Physical sciences #Fixed-point theorem #Fundamental theorem #Geometry #Hilbert space #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #No-go theorem #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum mechanics #Quantum state #Random Matrices and Applications #Regular polygon #Spectral Theory in Mathematical Physics #State (computer science) #Statistical Mechanics (cond-mat.stat-mech) #Tensor (intrinsic definition) #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1310.2200
Remarks 2.1 and 2.2 added
openalex publication_date 2013/10/08 · arxiv created 2014/08/22 · arxiv updated 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quantum de Finetti theorem asserts that the k-body density matrices of a N-body bosonic state approach a convex combination of Hartree states (pure tensor powers) when N is large and k fixed. In this note we review a construction due to Christandl, Mitchison, König and Renner valid for finite dimensional Hilbert spaces, which gives a quantitative version of the theorem. We first propose a variant of their proof that leads to a slightly improved estimate. Next we provide an alternative proof of an explicit formula due to Chiribella, which gives the density matrices of the constructed state as a function of those of the original state.