Unitary Correlation Sets

2016/12/31 by S.J. Harris, Samuel J. Harris, Vern I. Paulsen
Mathematics · #Combinatorics #Correlation #Discrete mathematics #Embedding #Embedding problem #Geometry #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Mathematics #Pure mathematics #Tensor (intrinsic definition) #Tensor decomposition and applications #Tensor product #Unitary state #math.OA #msc:46L99 #msc:47L25

paper · pdf · doi:10.1007/s00020-017-2383-9

published as Integral Equations and Operator Theory, Volume 89, Issue 1, 2017, pages 125--149 · 24 pages, fixed a small error in the proof of Theorem 5.3 (v2)

openalex publication_date 2017/06/09 · arxiv created 2018/01/10 · arxiv updated 2018/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The unitary correlation sets defined by the first author in conjunction with tensor products of U_nc(n) are further studied. We show that Connes' embedding problem is equivalent to deciding whether or not two smaller versions of the unitary correlation sets are equal. Moreover, we obtain the result that Connes' embedding problem is equivalent to deciding whether or not two cross norms on M_n ⊗ M_n are equal for all n ≥ 2.

Citations

• Characterisations of the weak expectation property
• Injectivity and operator spaces
• Universal entanglement transformations without communication
• Classification of Injective Factors Cases II 1 , II ∞ , III λ , λ � 1