Unitary Correlation Sets

Abstract

The unitary correlation sets defined by the first author in conjunction with tensor products of ${\mathcal{U}}_{nc}(n)$ 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 $M_n\otimes M_n$ are equal for all $n\ge 2$.

24 pages, fixed a small error in the proof of Theorem 5.3 (v2)

References in corpus (1)

• Connes' embedding problem and Tsirelson's problem

Cited by in corpus (5)

• The quantum-to-classical graph homomorphism game
• Non-closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla
• Connes' Embedding Problem and Winning Strategies for Quantum XOR Games
• Quantum Teleportation and Super-dense Coding in Operator Algebras
• Morphisms in categories of nonlocal games