2007/01/11 by Graeme Mitchison, Mitchison, Graeme
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0701064
12 pages, 1 figure
arxiv created 2007/01/11 · openalex publication_date 2007/01/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quantum de Finetti theorem says that, given a symmetric state, the state obtained by tracing out some of its subsystems approximates a convex sum of power states. The more subsystems are traced out, the better this approximation becomes. Schur-Weyl duality suggests that there ought to be a dual result that applies to a unitarily invariant state rather than a symmetric state. Instead of tracing out a number of subsystems, one traces out part of every subsystem. The theorem then asserts that the resulting state approximates the fully mixed state, and the larger the dimension of the traced-out part of each subsystem, the better this approximation becomes. This paper gives a number of propositions together with their dual versions, to show how far the duality holds.